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You may need to use the appropriate appendix table or technology to answer this question.

The following hypothesis test is to be conducted:

- **H0**: Median ≤ 170
- **Ha**: Median > 170

A sample of 30 provided 23 observations greater than 170, 1 observation equal to 170, and 6 observations less than 170. Use \(\alpha = 0.01\).

1. Find the value of the test statistic. (Round your answer to two decimal places.)
\( z = \)

2. Find the p-value. (Round your answer to four decimal places.)
p-value =

3. What is your conclusion?
- Do not reject H0. The population median is greater than 170.
- Reject H0. The population median is less than or equal to 170.
- Do not reject H0. The population median is less than or equal to 170.
- Reject H0. The population median is greater than 170.

Answer :

Final answer:

The value of the test statistic is 0 and the p-value is greater than 0.01. Therefore, we fail to reject the null hypothesis. The conclusion is that the population median is less than or equal to 170.

Explanation:

To find the value of the test statistic, we need to calculate the standard error of the median. Since the sample size is 30, we can use the formula:

Standard Error of Median = √(n/4)

where n is the sample size. Plugging in the values, we get:

Standard Error of Median = √(30/4) = √7.5 ≈ 2.74

Next, we calculate the test statistic (z-score) using the formula:

z = (Median - Hypothesized Median) / Standard Error of Median

Plugging in the values, we get:

z = (170 - 170) / 2.74 = 0

The value of the test statistic is 0.

To find the p-value, we compare the test statistic to the critical value. Since the alternative hypothesis is that the population median is greater than 170, we are conducting a one-tailed test. With a significance level () of 0.01, the critical value is approximately 2.33.

Since the test statistic (0) is less than the critical value (2.33), we fail to reject the null hypothesis. This means that there is not enough evidence to conclude that the population median is greater than 170.

Learn more about hypothesis testing for a population median here:

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