Norkers at a certain soda drink factory collected data on the volumes (n ounces)

Question

Norkers at a certain soda drink factory collected data on the volumes (n ounces) of a simple random sample of 19 cans of the soda drink Those volumes have a mean of that almost all cans have volumes between 1189 oz and 12 53 oz, the range nule 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 o.05 significance level Complete parts (a) through (d) below b. Compute the test statistic 12.19 oz and a standard deviation of 0.09 oz, and they appear to be from a normally distributed population If the workers want the filing process to work s Round to three decimal places as needed) c. Find the P-value P-value (Round to four decimal places as needed) d. State the conclusion Ho.because the P.value is ?ithe level of sigrncace There is ?|evidence toco cute mat tre popuanon standard

Explanation / Answer

The null and alternative hypothesis are:

H0: Population sd = 0.16

H1: Population sd < 0.16 (claim)

b) Test statistics:

Chi-square = (n - 1)*s2 / sd2 = (18*0.092) / 0.162 = 5.695

c) P-value:

By using excel function we can find out the P-value for left tailed test.

Since the alternative hypothesis contains less than sign so the test is left tailed test.

By using Chisq.dist function the P- value is 0.0027

d) State the conclusion:

Decision: If P-value > alpha(level of significance) then we fail to reject the null hypothesis otherwise reject the null hypothesis.

Here P-value (0.0027) is not greater than alpha(0.05) so reject the null hypothesis means in favor of an alternative that is claim.

Reject H0. Because the P-value is less than the level of significance. There is sufficient evidence to conclude that the population standard deviation of less than 0.16 oz

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