QuestionFind the test statistic $z$ for a sample mean of 84, size 49, standard deviation 14, testing if mean > 80 at $\alpha = 0.05$ .

Studdy Solution

STEP 1

Assumptions1. The null hypothesis is that the population mean is less than or equal to80. . The alternative hypothesis is that the population mean is greater than80.
3. The sample size is49.
4. The significance level (alpha) is0.05.
5. The sample mean is84.
6. The population standard deviation is14.

STEP 2

The test statistic for a hypothesis test about a population mean is given by the formula $z = \frac{\bar{x} - \mu}{\sigma / \sqrt{n}}$ where $\bar{x}$ is the sample mean, $\mu$ is the population mean under the null hypothesis, $\sigma$ is the population standard deviation, and $n$ is the sample size.

STEP 3

Now, plug in the given values into the formula to calculate the test statistic.
$z = \frac{84 -80}{14 / \sqrt{49}}$

STEP 4

implify the denominator.
$z = \frac{84 -80}{14 /7}$

STEP 5

Calculate the test statistic.
$z = \frac{84 -80}{2}$

STEP 6

Calculate the final value of the test statistic.
$z = \frac{4}{2} =2$ The test statistic $z$ value is2, so the correct answer is a)2.

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QuestionFind the test statistic $z$ for a sample mean of 84, size 49, standard deviation 14, testing if mean > 80 at $\alpha = 0.05$ .

Studdy Solution

STEP 1

Assumptions1. The null hypothesis is that the population mean is less than or equal to80. . The alternative hypothesis is that the population mean is greater than80.
3. The sample size is49.
4. The significance level (alpha) is0.05.
5. The sample mean is84.
6. The population standard deviation is14.

STEP 2

STEP 3

Now, plug in the given values into the formula to calculate the test statistic.
$z = \frac{84 -80}{14 / \sqrt{49}}$

STEP 4

implify the denominator.
$z = \frac{84 -80}{14 /7}$

STEP 5

Calculate the test statistic.
$z = \frac{84 -80}{2}$

STEP 6

Calculate the final value of the test statistic.
$z = \frac{4}{2} =2$ The test statistic $z$ value is2, so the correct answer is a)2.

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QuestionFind the test statistic zzz for a sample mean of 84, size 49, standard deviation 14, testing if mean > 80 at α=0.05\alpha = 0.05α=0.05.

Studdy Solution

STEP 1

Assumptions1. The null hypothesis is that the population mean is less than or equal to80. . The alternative hypothesis is that the population mean is greater than80.3. The sample size is49.4. The significance level (alpha) is0.05.5. The sample mean is84.6. The population standard deviation is14.

STEP 2

STEP 3

Now, plug in the given values into the formula to calculate the test statistic.z=84−8014/49z = \frac{84 -80}{14 / \sqrt{49}}z=14/49​84−80​

STEP 4

implify the denominator.z=84−8014/7z = \frac{84 -80}{14 /7}z=14/784−80​

STEP 5

Calculate the test statistic.z=84−802z = \frac{84 -80}{2}z=284−80​

STEP 6

Calculate the final value of the test statistic.z=42=2z = \frac{4}{2} =2z=24​=2The test statistic zzz value is2, so the correct answer is a)2.

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QuestionFind the test statistic $z$ for a sample mean of 84, size 49, standard deviation 14, testing if mean > 80 at $\alpha = 0.05$ .

Now, plug in the given values into the formula to calculate the test statistic.
$z = \frac{84 -80}{14 / \sqrt{49}}$

implify the denominator.
$z = \frac{84 -80}{14 /7}$

Calculate the test statistic.
$z = \frac{84 -80}{2}$

Calculate the final value of the test statistic.
$z = \frac{4}{2} =2$ The test statistic $z$ value is2, so the correct answer is a)2.