Question

Consider the hypotheses shown below.

Given that x overbar =57​, sigma =12​, n =35​, alpha =0.05​, complete parts a and b. Upper H 0​: muless than or equals 55 Upper H 1​: mugreater than 55

a. What conclusion should be​ drawn?

b. Determine the​ p-value for this test.

Answer 1

a)

The test hypothesis is

This is a one-sided test because the alternative hypothesis is formulated to detect the difference from the hypothesized mean on the upper side

Now, the value of test static can be found out by following formula:

Since the sample size is n = 35, degrees of freedom on the t-test statistic are n-1 = 35-1 = 34

This implies that

Since , we fail to reject the null hypothesis

b)

Using Excel's function =T.DIST.RT(t₀,n-1), the P-value for t₀ = 0.986 in an upper-tailed t-test with 34 degrees of freedom can be computed as