Question

Use the t-distribution and the sample results to complete the following test of the hypotheses. Use a 5% significance level.

Test Ho : μ = 500 vs Ha : μ ≠ 500 using the sample results x ¯ = 432, s = 118, with n = 75.

a) Discuss whether it is OK to use the t-distribution to determine the results of the test. The underlying distribution is skewed to the right with several outliers.

b) How many degrees of freedom are there in this test?

c) What is test statistic, t? Round to 3 decimal places. Show your work.

d) Is this a left-tailed, right-tailed, or two-tailed test?

e) What is the p-value? Round to 3 decimal places.

f) Would you reject or fail to reject the null hypothesis for this test?

Answer 1

Part a)

Since we have sample standard deviation, we can use t test / t distribution to calculate confidence interval.

Part b)

Degree of freedom = n - 1 = 74

Part c)

Test Statistic :-
t = ( X̅ - µ ) / ( S / √(n))
t = ( 432 - 500 ) / ( 118 / √(75) )
t = -4.991

Part d)

It is two tailed test

Part e)

P - value = P ( t > 4.9907 ) = 0.000

Part f)

Reject null hypothesis if P value < α = 0.05 level of significance
P - value = 0 < 0.05, hence we reject null hypothesis
Conclusion :- Reject null hypothesis