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Statistical errors

Related Topics

Wize University Statistics Textbook > Exploratory Data Analysis

Measures of Central Tendency

5 Activities

Wize University Statistics Textbook > Hypothesis Testing with One Sample

Type I and Type II Errors

6 Activities

Wize University Statistics Textbook > Hypothesis Testing with One Sample

Hypothesis Test for a Mean

4 Activities

Wize University Statistics Textbook > Estimating with Confidence Intervals

Margin of Error and Sample Size

2 Activities

Wize University Statistics Textbook > Estimating with Confidence Intervals

Confidence Interval for a Mean

3 Activities

For the following statements, select true or false. Enter T for True, F for False. (Use capital letters: T, F)


1. The mean weight of five cats is 20 lbs. We take away one that at weights 28 lbs. The mean weight of the remaining cats is 18 lbs.

2. The 95% confidence interval is [$800, $1,200]. The sample mean must be $1,000.

3. Increasing the sample size will decrease the margin of error while keeping the level of confidence unchanged.

4. Brenda concludes that hiring greeters at her store increased sales, but in fact it didn’t. She committed a Type I error.


More Measures of Central Tendency Questions:
Practice: Median
Practice: Median
(i) Where is the median of 50 numbers?
(ii) Where is the median of 51 numbers?
Statistics: Data transformation
You multiply all values in a data set by 55 and then add four. The resulting mean is 34 and the resulting standard deviation is 25.
Determine the mean and standard deviation of the original data.
Measure of Central Tendency: Transforming Data
You multiply all values in a data set by 55 and then add four. The resulting mean is 34 and the resulting standard deviation is 25.
Determine the mean and standard deviation of the original data.
Measures of Central Tendency
In the university bookstore, there are 25 chemistry books with a mean number of pages equaling 150, and 30 physics books with a mean number of pages equaling 220. Overall, what is the mean number of pages of all of the chemistry and physics books?
Measures of Central Tendency
We measure the height of 10 basketball players:
The mean is 195cm
The median is 195cm
Measures of Central Tendency
In the university bookstore, there are 25 chemistry books with a mean number of pages equaling 150, and 30 physics books with a mean number of pages equaling 220. Overall, what is the mean number of pages of all of the chemistry and physics books?
Transforming Data: Central tendency and variability
Practice: Transforming Data
You multiply all values in a data set by 55 and then add four. The resulting mean is 34 and the resulting standard deviation is 25.
Determine the mean and standard deviation of the original data.
Measures of central tendency
In a data set with six numbers, the smallest number and largest numbers are removed. Which of the following will not change?
i) Mean
ii) Median
Measures of Central Tendency
The mean weight of five cats is 20 lbs. We take away one that at weights 28 lbs. The mean age of the remaining cats is:
Measures of Central Tendency
In a group of 5 students, each spends on average 4 hours on their phone.
In another group of 9 students, each spends on average 3 hours on their phone.
In yet another group of 7 students, each spends on average 7 hours on their phone.
Measures of Central Tendency
The average of a sample of 12 numbers is 24. It turns out that some numbers were incorrectly entered. A number with value 7 was incorrectly entered as a 17 and a number with value 12 was incorrectly entered as an 11. Find the correct sample mean.
Statistics: Definitions
One of the following statements is false. Which one is it?
Measures of Central Tendency
(i) Where is the median of 50 numbers?
(ii) Where is the median of 51 numbers?
(iii) Find the median of 1, 2, 3, 4, 5, 8, 10, 14, 19, 22, 28, 40, 60, 70 (there are 14 numbers)
More Type I and Type II Errors Questions:
Type I and II Errors
When we reject the null hypothesis we are
Type I and II Errors
The power of a hypothesis test is
Type I and II Errors
Jimmy wants to sell his home. The null hypothesis is that by renovating his house he will not get more than 12 bids. Which of the following is true?
Type I and Type II Errors
Consider the following null and alternative hypotheses.
Ho: coffee doesn't help suppress appetite
Ha; coffee helps suppress appetite
Type I and Type II Errors
Consider the following null and alternative hypotheses:
H0: coffee doesn't help suppress appetite
Type I and Type II Errors
Campers contemplate whether the water at a nearby lake is safe for consumption or not.
Select the correct hypotheses.
(a)
Type I and Type II Errors
Mega Corp’s reduction in production costs is thanks to years of research and development. They boast on Forbes Magazine that this is why their prices now are lower.
Select the correct hypotheses.
(a)
Type I and Type II Errors
Brenda concludes that hiring greeters at her store increased sales, but in fact it didn't. This is an example of:
Type I and Type II Errors
The power of a hypothesis test is
Type I and Type II Errors
Jimmy wants to sell his home. The null hypothesis is that by renovating his house he will not get more than 12 bids. Which of the following is true?
Type I and II Errors
The mayor believes that the crime rate has stayed the same but in fact it is much worse.
Determine if a Type I Error, Type II Error, or correct decision has been made.
Type I and II Errors
Carbo Max determined that they developed a pill that allows people to eat carbs and not gain weight. However, people who tried it actually gained weight. Lawsuits ensued.
Determine if a Type I Error, Type II Error, or correct decision has been made.
Statistical Errors
What is the power of a hypothesis test?
Statistics: Definitions
One of the following statements is false. Which one is it?
More Hypothesis Test for a Mean Questions:
Confidence Interval for a Mean
A random sample of 30 credit card statements showed an average balance of $1,200 with a standard deviation of $135.
Hypothesis Testing: One-Tailed Z-Test
Ronald the Cat is a popular English TV Series show with historical average of 1.2 million viewers per episode and a standard deviation of 0.41 million. Lately, the actor behind the character Ronald has made some controversial comments over the internet. Over 9 random episodes since the comments, the average number of viewers per episode dropped to 0.95 million. The producer is worried that the mean number of viewers has dropped.
a) State the null and alternative hypotheses.
b) Compute the test-statistic
Hypothesis Testing: One-tailed T-test for the Mean
Ryan's English teacher gave him 70% on his essay. He thinks he deserves more. The principal of his school randomly selects 7 English teachers to grade his paper The mean grade assigned is 80% with a standard deviation of 8%.
Hypothesis Testing: One-tailed T-test for the Mean
Ryan's English teacher gave him 70% on his essay. He thinks he deserves more. The principal of his school randomly selects 7 English teachers to grade his paper The mean grade assigned is 80% with a standard deviation of 8%.
Hypothesis Testing: One-Tailed Z-Test
Ronald the Cat is a popular English TV Series show with historical average of 1.2 million viewers per episode and a standard deviation of 0.41 million. Lately, the actor behind the character Ronald has made some controversial comments over the internet. Over 9 random episodes since the comments, the average number of viewers per episode dropped to 0.95 million. The producer is worried that the mean number of viewers has dropped.
a) State the null and alternative hypotheses.
b) Compute the test-statistic
Hypothesis Testing: One-Tailed Z-Test
Ronald the Cat is a popular English TV Series show with historical average of 1.2 million viewers per episode and a standard deviation of 0.41 million. Lately, the actor behind the character Ronald has made some controversial comments over the internet. Over 9 random episodes since the comments, the average number of viewers per episode dropped to 0.95 million. The producer is worried that the mean number of viewers has dropped.
a) State the null and alternative hypotheses.
b) Compute the test-statistic
Hypothesis test for a mean
Normal cows weigh an average of 50 tons. The cows in Hippy’s Farm have a gluten-free diet. Do their cows weight differently from normal cows? We randomly selected a sample of 41 cows from Hippy’s Farm; they weigh an average of 54.7 tons with a variance of 64. Use the Significance level of 0.01
Hypothesis Testing: One-tailed T-test for the Mean
Ryan's English teacher gave him 70% on his essay. He thinks he deserves more. The principal of his school randomly selects 7 English teachers to grade his paper The mean grade assigned is 80% with a standard deviation of 8%.
Hypothesis testing for a mean
In testing Ho:μH_o:\mu = 20 against Ha:μH_a:\mu > 20 the p-value is 0.32. The sample mean was 22.
Which of the following are true?
Hypothesis Test for a Mean
Normal cows weight an average of 50 tons with a standard deviation of 25tons. The cows in Hippy’s Farm have a gluten-free diet. Do their cows weight differently from normal cows? (Yes, No)
We randomly selected a sample of 41 cows from Hippy’s Farm; they weight an average of 55.7 tons.
Hypothesis testing for a mean
In testing H0:μH_0:\mu = 20 against H1:μH_1:\mu > 20 the p-value is 0.32. The sample mean was 22.
Which of the following are true?
Hypothesis testing for a mean
Goldilocks is a picky eater. The perfect temperature for porridge is 88°C. She won’t eat it if it’s too hot or too cold. Based on a random sample of 30 bowls of porridge, the average sample temperature is 91°C. The temperature is normally distributed with a standard deviation of 3°C. Is there evidence that the temperature of porridge is not to her liking?
Hypothesis Test for a Mean
After the Pokemon Go upgrade, we hypothesize that UBC students play the game for more minutes than 30 minutes a day.
Hypothesis test for a mean
You wish to test H0:μ=29   H1:μ≠29H_0:\mu=29\ \ \ H_1:\mu\ne29
A 90% confidence interval for the population mean is (22, 28)\left(22,\ 28\right)
Which of the following is not true?
Confidence Interval for a Mean
A random sample of 30 credit card statements showed an average balance of $1,200 with a standard deviation of $135.
Hypothesis testing: Mean
(iii) What is the p-value?
Hypothesis Testing: Mean
(ii) Find the test-statistic.
Hypothesis Test for a Mean
(iv) Using a 5% significance level, select the correct conclusion.
Hypothesis Test for a Mean
Parts (i) to (v) are based on the following information:
Mirco Management Ltd. allows full-time employees to take 1-hour lunch breaks per shift; however, they believe that they take more than an hour on average. If this is the case, the company will hire more floor supervisors and increase surveillance. A random sample of 30 employees revealed a mean of 64.5 minutes with a standard deviation of 11 minutes.
(i) Select the correct null and alternative hypotheses:
Hypothesis Test for a Mean
The professor wishes to see if the average grade exceeds 70%. His p-value is 0.0245. Select the correct statement(s). [There may be more than one correct answer.]
Hypothesis Testing for a Mean
Parts (i) to (iii) pertains the the following information:
The marketing department states that the average spending at the store is $335, but they believe that customers are spending less money, on average. A random sample of 31 customers reveal a mean of $368 with a standard deviation of $128.
(iii) At the 5% significance level, what is the correct conclusion?
Hypothesis Testing for a Mean
Parts (i) to (iii) pertains the the following information:
The marketing department states that the average spending at the store is $335, but they believe that customers are spending less money, on average. A random sample of 31 customers reveal a mean of $302 with a standard deviation of $128.
(ii) What is the p-value?
Hypothesis Test for a Mean
Parts (i) to (iii) pertains the the following information:
The marketing department states that the average spending at the store is $335, but they believe that customers are spending less money, on average. A random sample of 31 customers reveal a mean of $368 with a standard deviation of $128.
(i) What are the correct hypotheses?
Statistics: Definitions
One of the following statements is false. Which one is it?
Hypothesis Test for a Mean (one-tail)
In 2013, the business department reported that the average monthly salary for co-op students is $2,960. Kenya randomly sampled 25 co-op students in the business department. The sample mean is $3,325 with a standard deviation of $940. Assume the population is normally distributed. At the significance level 𝜶 = 𝟎.𝟎𝟓, is there evidence that the monthly salary is higher now?
(a) Is this a z-test or a t-test?
(b) State the hypotheses:
Hypothesis Test (Mean) - Two-Sided Test
The average time it takes to find a parking spot at the mall is 11.5 minutes. However, the mall's property was recently rezoned. Has the average time to find a parking spot changed since the rezoning? Based on a random sample of 41 cars, the average time for shoppers to find a parking spot is 10.25 minutes with a standard deviation of 4.5 minutes. The significance level is α=0.05\alpha=0.05.
(a) Is this a z-test or a t-test?
(b) State the hypotheses:
More Margin of Error and Sample Size Questions:
Margin of Error and Sample Size
Approximately 70% of laptops in our sample have components that are made in China. How many laptops should you sample to estimate the true proportion with 95% confidence and a margin of error of 0.075?
Margin of Error and Sample Size
In a sample random sample of 20, the average is 18 and the standard deviation is 1.25. Let m1m_1 be the margin of error for a 95% confidence interval. Let m2m_2 be the margin of error for a 90% confidence interval. Calculate the value of m1−m2m_1-m_2
Margin of Error and Sample Size
Previous studies have shown that approximately 70% of laptops have components that
are made in Cina. How many laptops should you sample to estimate the true proportion with 95% confidence and a margin of error of 0.09?
Margin of Error and Sample Size
You wish to estimate the proportion of all laptops in Kanata that have components made in Cina. In a random sample of 12 laptops, 10 have components made in Cina.
The margin of error for a 95% confidence interval for the proportion of laptops made in Cina is
Margin of error and sample size
Professor Karl has two large statistics classes. He teaches one class in the morning and one in the evening. He samples students in both classes to assess his teaching performance. He uses their latest quiz marks for his assessment.
Here is some summarized statistics:
Assuming that the variances of the class quiz marks are equal, find the margin of error for a 95% confidence interval for the difference in the two means
Margin of Error and Sample Size
In a sample random sample of 20, the average is 18 and the standard deviation is 1.25. Let m1m_1 be the margin of error for a 95% confidence interval. Let m2m_2 be the margin of error for a 90% confidence interval. Calculate the value of m1−m2m_1-m_2
Margin of Error and Sample Size
A research group wants to estimate the number of transactions people make on their credit cards each month. The standard deviation is known to be 42 transactions. They want to construct a 95% confidence interval to estimate the mean number of transactions for October 2015 to within no more than 8 transactions.
Determine the sample size required.
What sample size is required if they want to use a 99% confidence interval?
Margin og Error and Sample Size
A statistician wishes to compute a 90% confidence interval for the average number of calories a typical adult consumes. He wishes to have a margin of error of no more than 10 calories. What is the minimum sample size he can use? The population standard deviation is 75.
Margin of Error
Increasing the sample size will decrease the margin of error while keeping the same level of confidence.
Margin of Error and Sample Size
A research group wants to estimate the number of transactions people make on their credit cards each month. The standard deviation is known to be 42 transactions. They want to construct a 95% confidence interval to estimate the mean number of transactions for October 2015 to within no more than 8 transactions.
Margin of Error and Sample Size
A statistician wishes to compute a 90% confidence interval for the average number of calories a typical adult consumes. He wishes to have a margin of error of no more than 10 calories. What is the minimum sample size he can use? The population standard deviation is 75.
Margin of Error and Sample Size
True or False?
1) Increasing n will increase the margin of error?
2) Increasing Zα2Z_{\frac{α}{2}} will increase the margin of error?
Margin of Error and Sample Size
In predicting the mean length of a species of snakes, how many times as many observations do we need to sample to cut the margin of error by a half without changing the level of confidence?
Confidence Interval for a Mean
Which statement is true about a 95% confidence interval [188,212]?
More Confidence Interval for a Mean Questions:
Confidence Interval for a Mean
A 90% confidence interval for the mean number of pairs of shoes Justine purchases every few years is (5, 17).
Confidence Interval for a Mean
You wish to test if being a member of a union increases hourly wages, in dollars, for the average construction worker. A sample of 18 construction workers' earnings were recorded prior to and after forming a union.
The results are: mean difference = −4.135-4.135 standard deviation of differences = 7.197.19
Compute a 95% confidence interval for the mean difference in the hourly wages
Confidence Interval for a Mean
You wish to test Ho:μ=29   Ha:μ≠29H_o:\mu=29\ \ \ H_a:\mu\ne29
A 90% confidence interval for the population mean is (22, 28)\left(22,\ 28\right)
Which of the following is NOT true?
Confidence Interval for a Mean
We have an SRS of 100 people. If about 95% of the data is between 193 and 393, find the 95% confidence interval.
Confidence Interval for a Mean
The 95% confidence interval is [$800, $1,200]. The sample mean must be $1,000.
Confidence interval for a mean
According to a sample of 100 apartment suites in Twin Pines, the sample mean rent is $970. The population standard deviation is $540. Construct a 99% confidence interval for the true population mean rent in Twin Pines.
(a) The mayor of Twin Pines says that the mean rent is only $700. Is this plausible?
(b) Helen lives in Twin Pines and says her rent is only $700. Is this plausible?
Confidence Interval for a Mean
A large software development firm recently relocated its facilities. Top management has encouraged their professional employees to engage in local service activities. Based on a random sample of 24 professionals, the sample mean is 16.75 hours. The population standard deviation is 2.4 hours.
A 95% confidence interval for the true mean number of hours of volunteer time is closest to:
Confidence interval for a mean
Kevin is the quality assurance manager for Gossip Girl dolls that talk gibberish until the AA batteries run out. The commercial for the toy says: “Over 300 hours of non-stop yapping!” He randomly selects 36 dolls and finds that they talk non-stop for about 275 hours on average until their batteries are drained. The number of hours is normally distributed with a standard deviation of 25 hours.
A bored and angry mother sues the company for false advertisement. Gio, the Marketing Director, defends himself in court by saying that the toys' average number of hours is not significantly different from 300. Use the confidence interval calculated in Question 9 to determine the conclusion of the two-tailed hypothesis test at the 5% level of significance.
Confidence Interval for a Mean
Kevin is the quality assurance manager for Gossip Girl dolls that talk gibberish until the AA batteries run out. The commercial for the toy says: “Over 300 hours of non-stop yapping!” He randomly selects 36 dolls and finds that they talk non-stop for about 275 hours on average until their batteries are drained. The number of hours are normally distributed with a standard deviation of 25 hours.
Construct a 95% confidence interval for the hours of non-stop yapping.
Confidence interval for a mean
A 90% confidence interval for the average length of a pregnancy is 33 to 38 weeks.
The correct conclusion is
Confidence Interval for a Mean
A sample of 61 households that have dogs reveal that an average of $140 is spent on dog food per month. The standard deviation of the sample is $115 per month.
Construct a 90% confidence interval for the monthly mean amount spent on dog food.
Confidence Interval
(v) Which of the following is/are true? (Check all that applies.)
Confidence intervals
A large software development firm recently relocated its facilities. Top management has encouraged their professional employees to engage in local service activities. Based on a random sample of 24 professionals, the sample mean is 16.75 hours and the standard deviation is 2.4 hours.
A 95% confidence interval for the true mean number of hours of volunteer time is closest to:
Confidence intervals
Based on a random sample size of 20 people with full-time jobs, the average time they spend in the shower each morning is 16 minutes with a standard deviation of 5 minutes. Construct a 95% confidence interval.
Population sampling
There are 600 Sephora locations in the United States. Christine randomly selected 40 stores, and then she randomly selected 100 customers from each of those stores. Less than 1% of her sample identified as heterosexual males. Based on her sample, the average spending at Sephora is $45. In addition, 340 customers in her sample revealed that they have VIB Rouge status, which the highest tier status that is reached when a customer spends $1,000 in a calendar year.
Which of the following is/are true? (Check all that applies.)
Population Sampling: Confidence Interval
Bob, a second-year student at Twin Pines University, is not very good at statistics. He wishes to infer about the average starting salary of recent graduates at Twin Pines University. His sample included 12 friends, all recent graduates, and it revealed a mean of $55,000. His 90% confidence interval is [39,116, 80,884].
Bob reports: "We conclude that 90% of recent graduates at Twin Pines University earn between $39,116 and $80,884."
List everything that is wrong about his statement. (Check all that applies.)
Confidence Interval for a Mean
Which statement is true about a 95% confidence interval [188,212]?
Confidence interval with t-distribution
A sample of 61 households that have dogs reveal that an average of $140 is spent on dog food per month with a standard deviation of $115 per month.
Confidence Interval for a Mean
A t distribution is used instead of the normal z distribution when
Confidence Interval for a Mean
A 90% confidence interval for the average length of a pregnancy is 33 to 38 weeks.
The correct conclusion is