Fractions and Decimals

Discrete Mathematics

Differential Equations

Solved on Sep 19, 2023

Claim that the standard deviation of adult male pulse rates is less than 10 beats/min. For a sample of 138 males, the standard deviation is $8.5$ beats/min. Find the test statistic.

STEP 1

Assumptions1. The population standard deviation is claimed to be less than10 beats per minute. . We have a sample of138 adult males.
3. The sample standard deviation is8.5 beats per minute.
4. We are assuming a normal distribution of the data.

STEP 2

The test statistic for the hypothesis test of a population standard deviation is given by the chi-square formula $\chi^2 = \frac{(n-1)s^2}{\sigma^2}$ where- $\chi^2$ is the test statistic, - $n$ is the sample size, - $s$ is the sample standard deviation, and- $\sigma$ is the population standard deviation.

STEP 3

Now, plug in the given values for the sample size, sample standard deviation, and population standard deviation to calculate the test statistic.
$\chi^2 = \frac{(138-1)(8.5)^2}{10^2}$

STEP 4

implify the equation.
$\chi^2 = \frac{137 \times72.25}{100}$

STEP 5

Calculate the test statistic.
$\chi^2 = \frac{9901.25}{100} =99.0125$ The value of the test statistic is99.0125.

Was this helpful?

Start learning now

Download Studdy AI Tutor now. Learn with ease and get all help you need to be successful at school.

Contact Influencer program Policy Terms