Question

Homestyle Pizza of Camp Verde, Arizona, provides baking instructions for its premade pizzas. According to the instructions, the average baking time is 12 to 18 minutes. If the times are normally distributed, the standard deviation for the times should be approximately 1.2 minutes. A random sample of 18 pizzas yielded the sample standard deviation s = 2.21 minutes.

At 1% significance level, do the data provide sufficient evidence to conclude that the standard deviation of baking times is less than 1.2 minutes?

Use (a) the critical value approach and (b) the P-value approach

(Note: Conclusion should be the same no matter the approach used)

For each test,

i) State your null and alternative hypotheses.

ii) What are the significance level and the p-value?

iii) Compute the test statistic

iv) What conclusion can you draw based on the data? Write a sentence. Include your test results.

v) Is there any difference?

Answer 1

i) Claim: The standard deviation of baking times is less than 1.2 minutes.

The null and alternative hypothesis is

ii) Level of significance = 0.01

iii) Sample size = n = 18

Sample standard deviation = s = 2.21

Test statistic is

P-value = P( ) = 0.0000

Degrees of freedom = n - 1 = 18 - 1 = 17

Critical value = 33.409 ( Using chi-square table)

Test statistic > critical value we reject null hypothesis.

P-value < 0.01 we reject null hypothesis.

iv) Conclusion: The standard deviation of baking times is less than 1.2 minutes.

v) There is NO any difference in two conclusions.