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Statistics: Definitions

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Wize University Statistics Textbook > Hypothesis Testing with One Sample

Hypothesis Test for a Mean

4 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

Introduction to Hypothesis Testing

2 Activities

Wize University Statistics Textbook > Exploratory Data Analysis

Measures of Central Tendency

5 Activities

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?
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:
Statistical errors
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.
T
2. The 95% confidence interval is [$800, $1,200]. The sample mean must be $1,000.
T
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?
Statistical errors
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.
T
2. The 95% confidence interval is [$800, $1,200]. The sample mean must be $1,000.
T
More Introduction to Hypothesis Testing Questions:
Hypothesis Testing
If the p-value is greater than the significance level we:
Hypothesis testing
When we reject the null hypothesis we are
Hypothesis Testing: Correlation
For the following statements, select true or false. Enter T for True, F for False.
Confidence Interval for a Mean
A t distribution is used instead of the normal z distribution when
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.
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)
Statistical errors
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.
T
2. The 95% confidence interval is [$800, $1,200]. The sample mean must be $1,000.
T