Question

show your work please

Students estimated the length of one minute without reference to a watch or clock, and the times (seconds) are listed below. Test the claim that these times are from a population with a mean equal to 60 seconds

63

84

42

62

49

62

58

55

69

49

Final answers

Hypopthesis

Test Statistic
p-value
Decision
Conclusion

Answer 1

Here, we have to use one sample t test for the population mean.

The null and alternative hypotheses are given as below:

H0: µ = 60 versus Ha: µ ≠ 60

This is a two tailed test.

The test statistic formula is given as below:

t = (Xbar - µ)/[S/sqrt(n)]

From given data, we have

µ = 60

Xbar = 59.3

S = 11.85139467

n = 10

df = n – 1 = 9

α = 0.05

Critical value = - 2.2622 and 2.2622

(by using t-table or excel)

t = (Xbar - µ)/[S/sqrt(n)]

t = (59.3 - 60)/[ 11.85139467/sqrt(10)]

t = -0.1868

P-value = 0.8560

(by using t-table)

P-value > α = 0.05

So, we do not reject the null hypothesis

There is sufficient evidence to conclude that these times are from a population with a mean equal to 60 seconds.