Question

Workers at a certain soda drink factory collected data on the volumes​ (in ounces) of a simple random sample of 24 cans of the soda drink. Those volumes have a mean of 12.19 oz and a standard deviation of 0.12 ​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 12.52 ​oz, the range rule of thumb can be used to estimate that the standard deviation should be less than 0.15 oz. Use the sample data to test the claim that the population of volumes has a standard deviation less than 0.15 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.

b. Compute the test statistic.

c. Find the​ P-value.

d. State the conclusion. ▼Do not reject/Reject Upper H0​, because the​ P-value is ▼less than or equal to/greater than the level of significance. There is▼insufficient/sufficient evidence to conclude that the population standard deviation of can volumes is less than 0.15oz

Answer 1

Below are the null and alternative Hypothesis,
Null Hypothesis, H0: σ = 0.15
Alternative Hypothesis, Ha: σ < 0.15

b)

Test statistic,
Χ^2 = (n-1)*s^2/σ^2
Χ^2 = (24 - 1)*0.12^2/0.15^2
Χ^2 = 14.72

c)

P-value Approach
P-value = 0.0956
As P-value >= 0.05, fail to reject null hypothesis.

d)
▼Do not reject H0​, because the​ P-value is equal greater than the level of significance. There is insufficient evidence to conclude that the population standard deviation of can volumes is less than 0.15oz