Question

A commercial bakery's ovens are designed to bake cakes at a temperature of 345.0 °F. The ovens are calibrated so that their temperatures should be normally distributed with a mean of 345.0 °F and a standard deviation of 4.2 °F. During a recent inspection, the bakery's quality control supervisor selected a random sample of 15 ovens and recorded their temperatures. She recorded her summary statistics in the following table.

test of ?=345.0 vs ?≠345.0the assumed standard deviation=4.2significance level of ?=0.05

Sample size	Sample mean	Standard error
?	?⎯⎯⎯	SE
15	342.2 °F	1.08444 °F

Complete the analysis by calculating the ?-value and making the decision. Give the ?-value precise to at least four decimal places.

The supervisor wants her results to be statistically significant at a level of ?=0.05. Use the data provided and the ?‑value you calculated to fill in the blanks and complete the sentences that form the supervisor's conclusion.

?=

The decision is to                          the                         hypothesis. There is                         evidence that the ovens'

mean temperature is                                            °F.

Answer 1

This is the two tailed test .

The null and alternative hypothesis is

H₀ : = 345

H_a : 345

Test statistic = t

= ( - ) / s / n

= (342.2 - 345) / 1.08444  

Test statistic = -2.582

df = 14

P-value = 0.0217

reject,null , sufficient , equal to 345 ^o F.