Question

A.

A supermarket claims that the average wait time at the checkout counter is less than 9 minutes. We can assume that the population is Normally distributed.

Consider

H0: mu >= 9

H1: mu < 9

A random sample of 50 customers yielded an average wait time of 8.2 minutes and a standard deviation of 2.5 minutes.

What is the value of the test statistic (tstat or t-sub-xbar)?

(Provide two decimal places)____________

B.

Let Z be a standard Normal random variable. Define    to be the number y such that P( Z > y ) =    (this is the standard definition).

What is P( Z <    )?

(i.e. what is the probability that a standard Normal variable takes a value below  ?) ___________

C.

A test is carried out at a significance level of 0.10. Which of these is correct?

		There is a probability of 0.1 that the H0 may be wrong
		When H0 is wrong, there is a 0.9 probability of rejecting the H0 due to random variations in the sample
		There is a probability of 0.1 that when H0 is wrong, we may still keep it
		When H0 is right, the probability of rejecting H0 due to the random variations in the sample is limited to 0.1

D.

A manufacturer claims that the average emissions of a particulate from a process is below 2 ppm on average.  Let mu be the process average.  The alternate hypothesis would be

		mu > 2
		mu < 2
		mu  2
		mu = 2

E.

We need to test whether a medicine had any effect on reducing cholesterol.  To do this, several patients were subjected to the medicine, and their cholesterol levels were measured before and after the medicine was given. With this data, the appropriate test would be

		matched sample t-test
		independent sample t-test
		F test
		chi-square goodness of fit test

Answer 1

A) Value of test static is

$t={\bar x-\mu\over s/\sqrt n}={8.2-9\over 2.5/\sqrt{50}}\approx -2. 26$

B) There are missing information

C) By definition of significance level

The correct statement is "There is a probability of 0.1 that the H0 may be wrong"

D)

The alternative hypothesis is $\mu<2$

E) Correct option is

" matched sample t-test"