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 0.010 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?

69

80

37

63

44

25

58

65

64

45

66

67

92

86

66

Answer 1

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

Rejection Region
This is two tailed test, for α = 0.01 and df = 14
Critical value of t are -2.977 and 2.977.
Hence reject H0 if t < -2.977 or t > 2.977

Test statistic,
t = (xbar - mu)/(s/sqrt(n))
t = (61.8 - 60)/(18.0127/sqrt(15))
t = 0.387

P-value Approach
P-value = 0.7046
As P-value >= 0.01, fail to reject null hypothesis.

Yes students are reasonable