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 0.10 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?

75

93

47

77

54

31

72

72

76

58

71

77

105

101

71

Identify the test statistic.
t =
​(Round to three decimal places as​ needed.)

The​ P-value is __
​(Round to four decimal places as​ needed.)

Answer 1

From the given sample,

We have given Sample size = 15

Sample mean xbar = 72 sec

Sample standard deviation s= 19.41

Here population standard deviation is not known and sample size is less than 30, so we will use one sample t test.

The hypotheses are

H₀: μ= 60 sec

H_a: μ ≠ 60 sec

This is two-sided test.

1. Test statistics:

Test statistics value (t) = (xbar – μ) / (s/√n) = (72 - 60)/(19.41/sqrt(15)) = 2.394

Test statistics value (t) = 2.394

2. P value = T.DIST.2T(2.394,14)= 0.0312….. (using Excel)

P value = 0.0312

Decision: Reject H₀ because the P- value is less than the significant level 0.10 so reject null hypothesis at 0.10 level of significant.

Conclusion: At 10% level of significance, there is sufficient evidence to claim that mean is different from 60 seconds. So, we can conclude that students are not reasonably good at estimating one​ minute.