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home / study / math / statistics and probability / statistics and probability questions and answers / a carpet company advertises that it will deliver your carpet within 15 days of purchase. a ... Question: A carpet company advertises that it will deliver your carpet within 15 days of purchase. A sample... (3 bookmarks) A carpet company advertises that it will deliver your carpet within 15 days of purchase. A sample of 49 past customers is taken. The average delivery time in the sample was 16.2 days. The standard deviation of the population is known to be 5.6 days. Using the critical value approach, test to determine if their advertisement is legitimate. Let α = .0392. What is type II error if actual mean of carpet delivery is 17

Answer 1

We have,

Sample parameters:

n = 49

Formulating the hypothesis for the claim:

H0:

Ha:

Using the z test statistic to test the hypothesis.

We use the z table to find z critical for a one tailed test, at

z critical = 1.76

Since 1.5 < 1.76, we fail to reject the null hypothesis and conclude that, the carpet company indeed does deliver within 15 days of purchase.

If actual mean off carpet delivery is 17, Type II error can be calculated as follows.

Type II error occurs when we fail to reject a null hypothesis when it is false.

Thus, z < 1.76

P(z < 1.76) = 0.9608

Critical sample mean for is as below,

is the critical sample mean for incorrectly failing to reject the null hypothesis.

Given the null hypothesis is false at

= 0.9292

Thus probability of type ii error is 92.92%.