Question

A group of students estimated the length of one minute without reference to a watch or​ clock, and the times​ (seconds) are listed below. Use a 0.05 significance level to test the claim that these times are from a population with a mean equal to 60 seconds. Does it appear that students are reasonably good at estimating one​ minute?

72

81

39

68

40

25

58

64

63

50

63

73

94

88

68

This is the appropriate sample data

What are the null and alternative​ hypotheses?

A.

H0​: μ=60 seconds

H1​: μ> 60 seconds

B.

H0​: μ≠ 60 seconds

H1​: μ= 60 seconds

C.

H0​: μ= 60 seconds

H1​: μ< 60 seconds

D.

H0​: μ= 60 seconds

H1​: μ≠ 60 seconds

Determine the test statistic.

​(Round to two decimal places as​ needed.)

Determine the​ P-value.

​(Round to three decimal places as​ needed.)

State the final conclusion that addresses the original claim.

(Reject/Fail to Reject) H0. There is (sufficient/not sufficient) evidence to conclude that the original claim that the mean of the population of estimates is 60 seconds (is/is not correct). It (appears/does not appear) that, as a​ group, the students are reasonably good at estimating one minute.

Answer 1

Below are the null and alternative Hypothesis,
Null Hypothesis, H0: μ = 60
Alternative Hypothesis, Ha: μ ≠ 60

Test statistic,
t = (xbar - mu)/(s/sqrt(n))
t = (63.0667 - 60)/(18.6795/sqrt(15))
t = 0.64

P-value Approach
P-value = 0.532
As P-value >= 0.05, fail to reject null hypothesis.

Fail to Reject) H0. There is (not sufficient) evidence to conclude that the original claim that the mean of the population of estimates is 60 seconds (is not correct). It (does not appear) that, as a​ group, the students are reasonably good at estimating one minute