Question

Take this quiz as you would take a quiz in class. After you are done, check your work against the answers given in the back of the book.For each exercise, perform the steps below.

a. Identify the claim and state Ho and Ha

b. Determine whether the hypothesis test is left-tailed, right-tailed, or two-tailed, and whether to use a z-test or a t-test. Explain your reasoning.

c. Find the critical value(s) and identify the rejection region(s).

d. Find the appropriate standardized test statistic.

e. Decide whether to reject or fail to reject the null hypothesis.

f. Interpret the decision in the context of the original claim.

[APPLET] The table shows the credit scores for 12 randomly selected adults who are considered high-risk borrowers before and two years after they attend a personal finance seminar. At α=0.01, is there enough evidence to support the claim that the personal finance seminar helps adults increase their credit scores? Assume the populations are normally distributed.

Accepted Answer

Identify the null and alternative hypotheses based on the claim. Since the claim is that the mean score for male students is less than that for female students, set up the hypotheses as: $$H_0$$: \mu_{male} \geq \mu_{female}$$ and H_a$$: \mu_{male} \u003c \mu_{female}$$. Determine the significance level $$\alpha = 0.05$$ and note the sample sizes (n$$_{male} = 49$$, n$$_{female} = 50$$), sample means ($$\bar{x}_{male} = 279$$, $$\bar{x}_{female} = 292$$), and population standard deviations ($$\sigma_{male} = 41$$, $$\sigma_{female} = 39$$). Calculate the test statistic for the difference between two means when population standard deviations are known, using the formula:

Z$$ = \frac{(\bar{x}_{male} - \bar{x}_{female}) - (\mu_{male} - \mu_{female})}{\sqrt{\frac{\sigma_{male}^2}{n_{male}} + \frac{\sigma_{female}^2}{n_{female}}}}$$

Since under the null hypothesis $$\mu_{male} - \mu_{female} = 0$$, simplify accordingly. Find the critical value for a left-tailed test at $$\alpha = 0.05$$ from the standard normal distribution (Z-distribution). Compare the calculated test statistic to this critical value to decide whether to reject or fail to reject the null hypothesis. Interpret the decision in the context of the original claim: if you reject H_0$, it supports the claim that the mean score for male students is less than that for female students; if you fail to reject H_0$, there is not enough evidence to support the claim.

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Key Concepts

Hypothesis Testing

Two-Sample Z-Test for Means

Significance Level and Decision Rule