Question
Solve only part E
(10 pts) In an advertisement, a pizza shop claims that its mean delivery time is less than 30 minutes. A random sample of 36 delivery times has a mean of 28.5 minutes and a standard deviation of 3.5 minutes. Is there enough evidence to support the claim at a.05? (a) Set up the null and alternative hypotheses. (b) Find the test statistic. (c) Find the rejection region and state your conclusion. (d) What is the P-value for this test? (e) Find the probability of type II error when the true mean is 29.
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Answer #1

Let mu denotes the true mean delivery time.

To test H0 : μ-30 against 1:μ<30

Here

sample mean ar{x} = 28.5

sample standard deviation s=3.

and sample size 2

The rejection region is : 30- Vn or 3.5 30to.05.35 уж to.05,35

e) P(Type II Error)

= P(Accept H0 when H0 is not true)

3.5 ー* to.05,35)

30-2to.o5,35) t0.05,35 3.5 y 36 y 36

30-29 P(Z < -t00535 ) = -ㄒㄧ- y 36

30-29 = P(Z < -1.68957) 3.5 y 36

=P(Z < 0.0247157)

0(0.0247157 )

0,509859 (ans)

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