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Hypothesis Test for a Mean (one-tail)

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Wize University Statistics Textbook > Hypothesis Testing with One Sample

Hypothesis Test for a Mean

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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:

(c) What is the critical value?



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(d) Find the test statistic:

(e) Find the p-value.



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(f) Select the correct conclusion:

i. We reject 𝐻o; there is evidence that the monthly salary is higher now.
ii. We reject 𝐻o; there is no evidence that the monthly salary is higher now.
iii. We fail to reject 𝐻o; there is evidence that the monthly salary is higher now.
iv. We fail to reject 𝐻o; there is no evidence that the monthly salary is higher now.













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(g) What would be the conclusion if 𝜶 = 𝟎. 𝟎𝟏?

i. We reject 𝐻o; there is no evidence that the monthly salary is higher now.
ii. We fail to reject 𝐻o; there is evidence that the monthly salary is higher now.
iii. We fail to reject 𝐻a; there is no evidence that the monthly salary is the same.
iv. We fail to reject 𝐻o; there is no evidence that the monthly salary is higher now.












(h) What does that say about the strength of the evidence?



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 (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