Question

8.4.11-T Assigned Media Question Help 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 o 09 and they appear to be from a normal distributed population in the workers want the filing process to work so that almost all cans have volumes between 11 91 and 12 47 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 001 significance level Complete parts (a) through (d) below a. Identify the nul and alternative hypotheses. Choose the correct answer below DA Ho G=0.14 OZ Hy #014 oz B. Hy 20.14 oz H, <014 oz o. Ho 0.14 02 H <0.14 02 C. Ho a > 0.14 oz H, 0.14 oz b. Compute the test statistic x2 = 6.198 (Round to three decimal places as needed) c. Find the P-value P-value (Round to four decimal places as needed) Enter your answer in the answer box and then click Check Answer

Answer 1

Solutions:

a)

D) H₀:σ=0.14 oz

H₁:σ<0.14 oz

b)

test statistic =

- - 1s

Here S² =sample variance = (0.09)²

σ² = Population variance = (0.14)²

n : sample size = 16

so putting all values in above test statistic we get

$\chi ^{2}$= 6.198

c)

p-value = p($\chi ^{2}$> 6.198)=  0.0238