You wish to test the following claim at a significance level of 0.02.

- $ H_0: \mu = 50.1 $
- $ H_1: \mu > 50.1 $

You believe the population is normally distributed, but you do not know the standard deviation. You obtain a sample of size 85 with a mean of 51.7 and a standard deviation of 8.2.

1. What is the test statistic for this sample? (Report your answer accurate to 3 decimal places.)

2. What is the p-value for this sample? (Report your answer accurate to 4 decimal places.)

This test statistic leads to a decision to:
- a. reject the null
- b. accept the null
- c. fail to reject the null

As such, the final conclusion is that:
- a. there is sufficient evidence to conclude that the population mean is equal to 50.1.
- b. there is not sufficient evidence to conclude that the population mean is equal to 50.1.
- c. there is sufficient evidence to conclude that the population mean is greater than 50.1.
- d. there is not sufficient evidence to conclude that the population mean is greater than 50.1.

The test statistic for this sample is 1.464. The p-value for this sample is 0.0742. The final conclusion is that there is not sufficient evidence to conclude that the population mean is greater than 50.1.

To calculate the test statistic, we use the formula:

test statistic = (sample mean - hypothesized mean) / (sample standard deviation / sqrt(sample size))

Plugging in the given values, we get:

test statistic = (51.7 - 50.1) / (8.2 / sqrt(85)) = 1.464

To find the p-value, we compare the test statistic to the critical value(s) corresponding to the given significance level. Since the alternative hypothesis is μ > 50.1, this is a one-tailed test.

Looking up the critical value for a significance level of 0.02 in a t-table with 84 degrees of freedom, we find it to be approximately 2.306.

Since the test statistic (1.464) is smaller than the critical value (2.306), we fail to reject the null hypothesis. This means that there is not sufficient evidence to conclude that the population mean is greater than 50.1.

Learn more about test statistic.

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