Question

Workers at a certain soda drink factory collected data on the volumes (in ounces) of a simple random sample of 16 cans of the soda drink. Those volumes have a mean of 12.19 oz and a standard deviation of 0.08 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 11.92 oz and 12.48 oz, the range rule of thumb can be used to estimate that the standard deviation should be less than 0.14 oz. Use the sample data to test the claim that the population of volumes has a standard deviation less than 0.14 oz. Use a 0.05 significance level. Complete parts (a) through (d) below. a. Identify the null and alternative hypotheses. Choose the correct answer below. O A. Ho: 0 >0.14 oz H: 0 = 0.14 oz | 0 C. Hp: 3 = 0.14 oz H: 0+0.14 oz OB. Ho: o = 0.14 oz H: 0 <0.14 oz OD. Ho: 020.14 oz H: 0 <0.14 oz b. Compute the test statistic. x=0 (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. V Ho, because the P-value is V the level of significance. There is evidence to conclude that the population standard deviation of can volumes is less than 0.14 oz.

Answer 1

The statistical software output for this problem is:

One sample variance summary hypothesis test: 02 : Variance of population Ho : 02 = 0.0196 HA: 02 < 0.0196 Hypothesis test results: Variance Sample Var. DF Chi-square Stat p-value 0.0064 15 4.8979592 0.007

Hence,

a) Hypotheses: Option B is correct.

b) Test statistic = 4.898

c) P - value = 0.0070

d) Reject; is less than sufficient