Question

answer please

An information technologist used a program called ping to measure the time (in milliseconds) taken to contact and receive a reply from another computer on the Internet. You wish to perform the following test about the population standard deviation, Ho: 0 = 300 vs. HA: 0 < 300. A random sample of 30 connection times gave a sample standard deviation of s = 225.5. Assume that the population of connection times is normally distributed. If you test this hypothesis at the 5% level of significance, which of the following is the critical value to use and what decision would you make? O A. 17.71; reject Ho B. 42.56; do not reject Ho C. 42.56; reject Ho D. 17.71; do not reject Ho

Answer 1

Answer:

A. 17.71; reject H₀

Solution:

Here, we have to use Chi square test for the population variance or standard deviation.

The null and alternative hypotheses for this test are given as below:

H₀: σ = 300 versus H_a: σ < 300

This is a lower tailed test.

The test statistic formula is given as below:

Chi-square = (n – 1)*S^2/ σ²

From given data, we have

n = 30

S = 225.5

σ = 300

Chi-square = (30 - 1)* 225.5^2 / 300^2

Chi-square = 16.39

We are given

Level of significance = α = 0.05

df = n – 1

df = 29

Lower Critical value = 17.71

(by using Chi square table or excel)

Test statistic = 16.39 < 17.71

So, we reject the null hypothesis