Question

Part III: Hypothesis Testing Complete The Hypothesis Test Of Interest Using The Specified Approach. Test At The 5% Level Of Significance. Many Bank Employees Are Paid By The Hour. Consider A Small Bank Called BBBanking Which Is Currently Hiring. During The Interviewing Process. BBBanking's Manager Indicates That It Pays Its

Answer 1

Final Answer:

Based on the hypothesis test conducted at the 5% level of significance, we fail to reject the manager's claim that BBBanking pays its employees an average hourly wage of $25.

Step-by-step explanation:

The hypothesis test involves comparing the sample mean to the claimed population mean. Let's denote:

-
`\( H_0 \)`: The population mean hourly wage is $25.

-
`\( H_a \)`: The population mean hourly wage is not $25.

We conduct a t-test for the population mean:

`\[ t = \frac{\bar{x} - \mu_0}{(s)/(√(n))} \]`

where:

- \
`( \bar{x} \)`is the sample mean,

-
`\( \mu_0 \)`is the claimed population mean,

-
`\( s \)` is the standard deviation of the sample, and

-
`\( s \)`is the sample size.

In this case, with
`\( \bar{x} = $24.50 \),`
`\( \mu_0 = $25 \),`
`\( s = $3.50 \),` and
`\( n = 36 \),` we calculate the t-statistic. After comparing the t-statistic to the critical t-value at a 5% significance level with 35 degrees of freedom, we find that the calculated t-statistic does not fall in the rejection region. Therefore, we fail to reject the null hypothesis.

This means there is not enough evidence to conclude that the average hourly wage is different from $25, supporting the manager's claim. It's essential to consider the p-value and critical value in making this decision.

Answer 2

The question pertains to performing a hypothesis test at a 5% level of significance in the context of a bank's employee pay rates. To answer, one would state hypotheses, calculate a test statistic, determine the p-value, and make a decision based on comparing the p-value to the level of significance. Additional information is necessary to complete the test.

Step-by-step explanation:

The subject of the question is hypothesis testing, which is a statistical method used to decide whether to accept or reject a hypothesis based on sample data. The 5% level of significance indicates that there is a 5% risk of concluding that a difference exists when there is no actual difference (Type I error). In hypothesis testing, a p-value is calculated from the sample data and compared to the level of significance. If the p-value is less than the level of significance, the null hypothesis is rejected in favor of the alternative hypothesis.

To complete the hypothesis test for BBBanking's manager's claim about pay rates, the steps are as follows:

State the null hypothesis (H0), which typically represents no change or no effect, and the alternative hypothesis (H1), which represents a change or an effect that we aim to detect.

Collect the sample data and calculate the appropriate test statistic based on the type of data and the hypothesis being tested.

Determine the p-value associated with the test statistic.

Compare the p-value to the specified level of significance. If the p-value is less than 0.05 (5% level), we reject the null hypothesis.

The question is incomplete as it does not provide the specific claim of the manager or the sample data. To fully answer, additional information would be needed to conduct the hypothesis test.