Question

Workers at a certain soda drink factory collected data on the volumes (in ounces) of simple random sample of 15 cans of the soda drink Those volumes have mean of 12.19 oz and a standard deviation of 0.14 oz and they appear be from a normally distributed population. If the workers Want the filling process to work so that almost all cans have volume between 11.88 and 12.52, and the standard deviation should be less than 0.16 oz. use the sample data test that claim that the population of volumes has a standard deviation less than 0.16. Use a 0.025 significance level. what is the P- value ?

Workers at a certain soda drink factory collected data on the volumes (in ounces) of a simple random sample of 15 cans of the soda drink. Those volumes have a mean of 12.19 oz and a standard deviation of 0 14 oz, and they appear to be from a normally distributed population. If the workers want the filling process to work so that almost all cans have volumes between 11.88 oz and 12.52 oz, the range rule of thumb can be used to estimate that the standard deviation should be less than 0.16 oz. Use the sample data to test the claim that the population of volumes has a standard deviation less than 0.16 oz. Use a 0.025 significance level. Completo parts (a) through (d) below. a. Identify the null and alternative hypotheses. Choose the correct answer below. O A. Ho >0.16 oz B. Ho q=0.16 oz H, 30.16 oz Ho<0.16 02 OC. Ho a=0.16 oz OD. H: 20.16 oz H, #0.16 oz Hy <0.16 oz b. Compute the test statistic x = 10719 (Round to three decimal places as needed.) c. Find the P-value P-value = (Round to four decimal places as needed)

Answer 1

Answer:

P-value = 0.2920

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:

Null hypothesis: H₀: the population of volumes has a standard deviation of 0.16.

Alternative hypothesis: H_a: the population of volumes has a standard deviation less than 0.16.

H₀: σ = 0.16 oz

H₁: σ < 0.16 oz

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 = 15

S = 0.14

σ = 0.16

Chi-square = (15 - 1)*0.14^2/0.16^2

Chi-square = 10.719

We are given

Level of significance = α = 0.025

df = n – 1

df = 14

Critical value = 5.6287

(by using Chi square table or excel)

P-value = 0.2920

(by using Chi square table or excel)

P-value > α = 0.025

So, we do not reject the null hypothesis

There is not sufficient evidence to conclude that the population variance is the population of volumes has a standard deviation less than 0.16.