A facilities manager at a university reads in a research report that the mean amount of time spent in the shower by an adult is 5 minutes. He decides to collect data to see if the mean amount of time that college students spend in the shower is significantly different from 5 minutes. In a sample of 15 students, he found the average time was 4.61 minutes and the standard deviation was 0.75 minutes. Using this sample information, conduct the appropriate hypothesis test at the 0.05 level of significance. Assume normality. a) What are the appropriate null and alternative hypotheses? Но: х = 5 versus Ha: x # 5 5 versus Ha: H< 5 Но: и 5 versus Ha: l > 5 Но: и Но: и 5 versus Ha: l # 5 b) What is the test statistic? Give your answer to four decimal places. -2.0140 c) What is the P-value for the test? Give your answer to four decimal places. 1.9560 X d) What is the appropriate conclusion? Fail to reject the claim that the mean time is 5 minutes because the P-value is larger than 0.05 Fail to reject the claim that the mean time is 5 minutes because the P-value is smaller than 0.05. Reject the claim that the mean time is 5 minutes because the P-value is smaller than 0.05 Reject the claim that the mean time is 5 minutes because the P-value is larger than 0.05

Question
A facilities manager at a university reads in a research report that the mean amount of time spent in the shower by an
adult is 5 minutes. He decides to collect data to see if the mean amount of time that college students spend in the shower
is significantly different from 5 minutes. In a sample of 15 students, he found the average time was 4.61 minutes and the
standard deviation was 0.75 minutes. Using this sample information, conduct the appropriate hypothesis test at the 0.05
level of significance. Assume normality.
a) What are the appropriate null and alternative hypotheses?
Но: х
= 5 versus Ha: x # 5
5 versus Ha: H< 5
Но: и
5 versus Ha: l > 5
Но: и
Но: и
5 versus Ha: l # 5
b) What is the test statistic? Give your answer to four decimal places. -2.0140
c) What is the P-value for the test? Give your answer to four decimal places. 1.9560
X
d) What is the appropriate conclusion?
Fail to reject the claim that the mean time is 5 minutes because the P-value is larger than 0.05
Fail to reject the claim that the mean time is 5 minutes because the P-value is smaller than 0.05.
Reject the claim that the mean time is 5 minutes because the P-value is smaller than 0.05
Reject the claim that the mean time is 5 minutes because the P-value is larger than 0.05

Image Transcription

A facilities manager at a university reads in a research report that the mean amount of time spent in the shower by an adult is 5 minutes. He decides to collect data to see if the mean amount of time that college students spend in the shower is significantly different from 5 minutes. In a sample of 15 students, he found the average time was 4.61 minutes and the standard deviation was 0.75 minutes. Using this sample information, conduct the appropriate hypothesis test at the 0.05 level of significance. Assume normality. a) What are the appropriate null and alternative hypotheses? Но: х = 5 versus Ha: x # 5 5 versus Ha: H< 5 Но: и 5 versus Ha: l > 5 Но: и Но: и 5 versus Ha: l # 5 b) What is the test statistic? Give your answer to four decimal places. -2.0140 c) What is the P-value for the test? Give your answer to four decimal places. 1.9560 X d) What is the appropriate conclusion? Fail to reject the claim that the mean time is 5 minutes because the P-value is larger than 0.05 Fail to reject the claim that the mean time is 5 minutes because the P-value is smaller than 0.05. Reject the claim that the mean time is 5 minutes because the P-value is smaller than 0.05 Reject the claim that the mean time is 5 minutes because the P-value is larger than 0.05

Expert Answer

Want to see the step-by-step answer?

See Answer

Check out a sample Q&A here.

Want to see this answer and more?

Experts are waiting 24/7 to provide step-by-step solutions in as fast as 30 minutes!*

See Answer
*Response times vary by subject and question complexity. Median response time is 34 minutes and may be longer for new subjects.

Related Statistics Q&A

Find answers to questions asked by student like you
Show more Q&A

Q: Part D and E

A: In order to get the test statistic value, the MINITAB output for the paired t-test is given below.

Q: Please show TI 84 steps

A: Introduction:The 100 (1 – α) % confidence interval for the population mean, μ, for given population ...

Q: Question Seventy cards are numbered 1 through 70, one number per card. One card is randomly selec...

A: Define the given events A as multiples of 3 and B as multiples of 5.The events A and B are as follow...

Q: Births are approximately uniformly distributed between the 52 weeks of the year. 1 1 s x53 f(x) 52 (...

A: Solution:Continuous uniform distribution:A random variable X is said to have the rectangular distrib...

Q: 4. Suppose a new sample is chosen and you got the following estimated OLS line: predicted birthweigh...

A: Introduction:Effect of scale change of the predictor, on the regression coefficients:Suppose x denot...

Q: Suppose you flip eight fair coins.   What is the probability of flipping exactly eight heads? What...

A: Binomial distribution:The events that has exactly two possible outcomes (success or failure) follows...

Q: Possion Distribution The number of calls received by an office on Monday morning between 8:0...

A: Let us define the random variable X as the number of calls received by on Monday morning between 8:0...

Q: An automobile manufacturer finds that 1 in every 2000 automobiles produced has a particular manufact...

A: It is given that n =5,000 and p = 0.0005 (=1/2,000).The probability mass function of binomial distri...

Q: (Round to two decimal places as needed.) d. Find P p>0 43) The probability that p is greater than 0....

A: The provided data is sample size, n is 77 and the probability of success, p is 0.4.The mean and stan...