Question

Perform hypothesis tests on the following five problems.

Assume that a simple random sample has been selected from a normally distributed population and test the given claim. Identify the hypotheses, test statistic, critical value(s), decision about the null hypothesis, and final conclusion.

1. The age of actresses when they won an acting award is summarized by the statistics n = 78, ?̅ = 35.3 years, and s = 11.9 years. Use a 0.05 significance level to test the claim that the mean age of actresses when they win an acting award is 34 years.

Answer 1

Step 1:

Ho : = 34

Ha: 34

Null hypothesis states that the mean age of actresses when they win an acting award is 34 years.

Alternative hypothesis states that the mean age of actresses when they win an acting award is not equal 34 years.

Step 2: Test statistics

n = 78

sample mean = 35.3

sd = 11.9

Assuming data is normally distrbuted and also as population sd is not given, we will calculate t stat.

t = -0.965

Step 3: Decision

df = 78-1 = 77

= 0.05

t critical (two tailed test) = +/- 1.991

As the t stat (-0.965) does not fall in the rejection area, we fail to reject the Null hypothesis.

Hence we do not have sufficient evidence to believe that mean age of actresses when they win an acting award is not equal 34 years.