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

0.100 significance level to test the claim that these times are from a population with a mean equal to 60 seconds. Determine the test statistic

69

82

39

62

41

22

58

64

68

47

62

67

92

88

68

Answer 1

Answer)

Null hypothesis Ho : u = 60

Alternate hypothesis Ha : u not equal to 60

First we need to find the mean and s.d of the given data

Mean = 61.9

S.d = 18.8

N = 15

Test statistics t = (sample mean - claimed mean)/(s.d/√n)

t = (61.9 - 60)/(18.8/√15) = 0.391

As the population standard deviation is unknown here we will use t distribution to estimate the p-value

Degrees of freedom is = n-1 = 14

For 14 dof and 0.391 test statistics

P-value from t distribution is = 0.7017

As the obtained p-value is greater than the given significance

we fail to reject the null hypothesis

So we have enough evidence to conclude that mean is 60