Question

1. A college statistics instructor claims that the mean age of college statistics students is 24. A random sample of 116 college statistics students revealed a mean age of 22.7. The population standard deviation is known to be 5.68 years. Test his claim at the 0.05 level of significance.

1. State the hypotheses and identify the claim.

2. Find the critical value(s)

3. Compute the test value.

4. Make the decision to reject or not reject the null hypothesis.

5. Summarize the results.

Answer 1

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

The null and alternative hypotheses are given as below:

Null hypothesis: H₀: the mean age of college statistics students is 24.

Alternative hypothesis: H_a: the mean age of college statistics students is not 24.

H₀: µ = 24 versus H_a: µ ≠ 24

This is a two tailed test.

The test statistic formula is given as below:

Z = (Xbar - µ)/[σ/sqrt(n)]

From given data, we have

µ = 24

Xbar = 22.7

σ = 5.68

n = 116

α = 0.05

Critical value = -1.96 and 1.96

(by using z-table or excel)

Z = (22.7 - 24)/[5.68/sqrt(116)]

Z = -2.4650

P-value = 0.0137

(by using Z-table)

P-value < α = 0.05

So, we reject the null hypothesis

There is not sufficient evidence to conclude that the mean age of college statistics students is 24.