108k views
3 votes
Fowle Marketing Research, Inc., bases charges to a client on the assumption that telephone surveys can be completed in a mean time of 15 minutes or less. If a longer mean survey time is necessary, a premium rate is charged. Suppose a sample of 35 surveys shows a sample mean of 17 minutes. Use = 4 minutes. Is the premium rate justified? Click on the datafile logo to reference the data. a. Formulate the null and alternative hypotheses for this application. H 0: H a: b. Compute the value of the test statistic (to 2 decimals). c. What is the p-value (to 4 decimals)? d. Using = .01, is a premium rate justified for this client?

1 Answer

6 votes

Answer:

Test statistics = 2.96

P-value = 0.35%

Yes, a premium rate is justified for this client

Explanation:

We are given that a sample of 35 surveys shows a sample mean of 17 minutes and standard deviation of 4 minutes.

Also, we have to test that whether telephone surveys can be completed in a mean time of 15 minutes or less or not.

Null Hypothesis,
H_0 :
\mu <= 15 minutes {means that the telephone surveys can be completed in a mean time of 15 minutes or less}

Alternate Hypothesis,
H_1 :
\mu > 15 minutes {means that the telephone surveys take more than mean time of 15 minutes to get completed}

The test statistics we will use here is;

T.S. =
(Xbar-\mu)/((s)/(√(n) ) ) ~
t_n_-_1

where, X bar = sample mean = 17 minutes

s = sample standard deviation = 4 minutes

n = sample size = 35

So, Test statistics =
(17-15)/((4)/(√(35) ) ) ~
t_3_4

= 2.96

At 1% significance level, t table gives critical value of 2.441 at 34 degree of freedom. Since our test statistics is more than the critical value as 2.958 > 2.441 so we have sufficient evidence to reject null hypothesis as our test statistics will fall in the rejection region.

P-value is given by, P(
t_3_4 > 2.96) = 0.0035 or 0.35%

Here also, P-value is less than the significance level as 0.035% < 1% , so will reject null hypothesis.

Therefore, we conclude that the telephone surveys take more than mean time of 15 minutes to get completed and due to which a premium rate is charged and a premium rate is justified for this client.

User Bryen
by
7.4k points
Welcome to QAmmunity.org, where you can ask questions and receive answers from other members of our community.

9.4m questions

12.2m answers

Categories