Question

A.

A supermarket claims that the average wait time at the checkout counter is less than 9 minutes.  Assume that we know that the standard deviation of wait times is 2.5 minutes. We will test at 5% level of significance.

Consider

H0: mu >= 9

H1: mu < 9

A random sample of 50 customers yielded an average wait time of 8.2 minutes.

What is the critical value for the Zstat (the Z-test statistic)?

(Provide two decimal places)____________

B.

Given the following hypotheses:

H0: the average return on stocks is at least 7%

H1: the average return on stocks is less than 7%

We take a random sample of stocks, find their returns, compute a test statistic, and make a conclusion at 5% level of significance.

What would be the type II error in this case?

		Average return on stocks is at least 7%, but we conclude that it is less than 7%
		Average return on stocks is less than 7%, but we conclude it is at least 7%
		Average return on stocks is less than 7%, and we conclude that it is less than 7%
		Average return on stocks is at least 7%, and we conclude that it is at least 7%

C.

A manager is trying to make a decision on investing in advertising based on whether they have a market share of at least 50%. A test of hypothesis is done as given below:

H0: p <= 0.5

H1: p > 0.5

where p is the proportion of the customers who use the company's product (that is, p is the market share of the company). The analyst proposes using a significance level of 0.05, but the manager wants to use 0.01. Which of the following statements is NOT correct:

		Using 0.01 instead of 0.05 decreases the type II error probability
		when H0 is right, using 0.01 instead of 0.05 reduces the error of rejecting H0
		using 0.05 instead of 0.01 increases type I error probability

D.

A manager of a supermarket believes that self-check out lanes lead to higher customer satisfaction. To test this, satisfaction ratings were collected from a group of customers prior to the introduction of the lanes, and from an independent group of customers after the lanes were introduced. Which of the following tests would be appropriate?

		matched sample t test
		F test of variance from two Normal populations
		chi square test of variance
		independent samples t test

E.

To test whether a coin is biased, we have these hypotheses:

H0: p = 0.5,

H1: p is not 0.5,

where p is the population proportion of "heads" when the coin is tossed.

A random sample of 50 tosses resulted in 15 heads. What is the value of the test statistic (Zstat) for this sample? (Provide two decimal places)_____________

Answer 1

A.

Critical value = -1.64

B.

Type II error is the probability of accepting H₀ when actually H₁ is true

Correct option : Average return on stocks is less than 7%, but we conclude it is at least 7%

C.

The statement which is NOT correct :

Using 0.01 instead of 0.05 decreases the type II error probability

D.

Since, the two samples are independent to each other, we use Independent samples test

Correct option : independent samples t test

E.

p0 = 0.5

n = 50

Z-statstic = -2.83