# Think of a vending machine on campus. The vending machine has a coin collector that should be emptied regularly. In the past, the vending machine company emptied the coin collector every 14 days, and recorded the weight of the coin collector when it is emptied. In the past 100 visits, the average weight of the coin collector was 22.5 pounds and the standard deviation was 20.

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Question 1

Think of a vending machine on campus. The vending machine has a coin collector that should be emptied regularly. In the past, the vending machine company emptied the coin collector every 14 days, and recorded the weight of the coin collector when it is emptied. In the past 100 visits, the average weight of the coin collector was 22.5 pounds and the standard deviation was 20.

If the coin collector is full, the vending machine is unusable. But emptying the collector is also an expense. The company finds that it is optimal to empty a coin collector when it weighs 20 pounds. The company wants to test the following hypotheses:

Null hypothesis: the mean weight of the coin collector emptied every 14 days is 20 pounds.

Alternative hypothesis: the mean weight of the coin collector emptied every 14 days is not 20 pounds.

Find the t-statistic of the test, and determine if the null hypothesis is rejected at the significance level of 5%. (Round the t-statistic to the second decimal place.)

a.

t-statistic is 2.5, so the null hypothesis is not rejected

b.

t-statistic is 1.25, so the null hypothesis is not rejected.

c.

t-statistic is 2, so the null hypothesis is rejected.

d.

t-statistic is 2.5, so the null hypothesis is rejected.

e.

t-statistic is 2, so the null hypothesis is not rejected.

f.

t-statistic is 1.25, so the null hypothesis is rejected.

1 points

Question 2

An inventor has developed a new, energy-efficient lawn mower engine.

He claims that the engine will run continuously for 300 minutes on a single gallon of regular gasoline.

From his stock of engines, the inventor selects a random sample of 100 engines for testing.

The engines run for an average of 294 minutes, with a standard deviation of 25 minutes.

The null hypothesis is that the mean run time is 300 minutes, and the alternative hypothesis is that the mean run time is NOT 300 minutes.

At different levels of significance, what is the result of the hypothesis test?

a.

The null hypothesis is rejected at 10% and 5%, but not rejected at 1%.

b.

The null hypothesis is rejected at 1%, 5% and 10%.

c.

The null hypothesis is rejected at 10%, but not rejected at 5% and 1%.

d.

The null hypothesis is not rejected at 1%, 5% and 10%.

e.

The null hypothesis is rejected at 1% and 5%, but not rejected at 10%.

f.

The null hypothesis is rejected at 1%, but not rejected at 5% and 10%.

1 points

Question 3

Suppose that the mean weight of King Penguins found in an Anarctic colony last year was 15.4 kilograms and the standard deviation was 2.5 kilograms.

You want to test the null hypothesis that the mean penguin weight this year does not differ from last year.

Assume that the standard deviation has not changed.

You are planning to measure a random sample of 100 penguins.

At 1% significance level, find the critical values for the test.

a.

14.990 and 15.810

b.

14.884 and 15.916

c.

14.910 and 15.890

d.

14.755 and 16.045

e.

15.008 and 15.792

1 points

Question 4

The Big Bang Theory is one of the most popular TV shows. You believe that 50% of all Americans who are 18 to 49 years old have watched the Big Bang Theory last Thursday night. You found a survey result that, of 400 respondents who are between 18 and 49 years old, 212 watched the Big Bang Theory last Thursday.

Then, what is the p-value of your hypothesis?

a.

0.16151

b.

0.42371

c.

0.31731

d.

0.54851

e.

0.23014

1 points

Question 5

The production manager of a company has asked for your assistance in analyzing a production process.

This process involves drilling holes whose diameters have to be 2 inches.

A random sample of 100 measurements had a sample mean of 1.97 inches and a standard deviation of 0.1 inches.

The null hypothesis that you are going to test is that the mean of drilling hole diameters is 2 inches, and the alternative hypothesis is the negation of the null hypothesis.

Find the p-value.

0.27%

21.13%

1.242%

31.732%

4.55%

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