## Related questions with answers

Perform each of the following steps.

a. State the hypotheses and identify the claim. b. Find the critical value(s). c. Find the test value. d. Make the decision. e. Summarize the results.

Use the traditional method of hypothesis testing unless otherwise specified.

A survey of 800 randomly selected recent degree recipients found that 155 received associate degrees; 450, bachelor degrees; 20, first professional degrees; 160, master degrees; and 15, doctorates. Is there sufficient evidence to conclude that at least one of the proportions differs from a report which stated that $23.3 \%$ were associate degrees; $51.1 \%$, bachelor degrees; $3 \%$, first professional degrees; $20.6 \%$, master degrees; and $2 \%$, doctorates? Use $\alpha=0.05$

Solution

Verified$\textbf{(a)}$

The hypotheses we wish to test are:

$H_{0}:$ The distribution of degree recipients is:

associate degrees, $23.3\%$; bachelor degrees, $51.1\%$; first professional degrees, $3\%$; master degrees, $20.6\%$; and doctoral degrees, $2\%$.

$H_{1}:$ The distribution of degree recipients is different from the distribution stated in the null hypothesis. (claim)

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