A software company is trying to decide whether to produce an upgrade of one of its programs. Customers would have to pay $100 for the upgrade. For the upgrade to be profitable, the company has to sell it to more than 20% of their customers. You contact a random sample of 60 customers and find that 16 would be willing to pay$100 for the upgrade. Which would be a more serious mistake in this setting-a Type I error or a Type II error? Justify your answer.

M. Goodisman et al. studied patterns in queen and worker wasps and published their findings in the article “Mating and Reproduction in the Wasp Var/min germanica”. The number of male mates of a queen wasp has a Poisson distribution with parameter $\lambda=2.7$. Find the probability that the number, Y, of male mates of a queen wast is a. exactly two. b. at most two. c. between one and three, inclusive. d. On average, how many male mates does a queen wasp have? e. Construct a table of probabilities for the random variable Y. Compute the probabilities until are zero to three decimal places. f. Draw a historgram of the probabilities in part (e).

"I can't get through my day without coffee" is a common statement from many college students. They assume that the benefits of coffee include staying awake during lectures and remaining more alert during exams and tests. Students in a statistics class designed an experiment to measure memory retention with and without drinking a cup of coffee 1 hour before a test. This experiment took place on two different days in the same week (Monday and Wednesday). Ten students were used. Each student received no coffee or one cup of coffee 1 hour before the test on a particular day. The test consisted of a series of words flashed on a screen, after which the student had to write down as many of the words as possible. On the other day, each student received a different amount of coffee (none or one cup). One of the researchers suggested that all the subjects in the experiment drink no coffee before Monday's test and one cup of coffee before Wednesday's test. Explain to the researcher why this is a bad idea and suggest a better method of deciding when each subject receives the two treatments.

Select the best answer. Are TV commercials louder than their surrounding programs? To find out, researchers collected data on 50 randomly selected commercials in a given week. With the television's volume at a fixed setting, they measured the maximum loudness of each commercial and the maximum loudness in the first 30 seconds of regular programming that followed. Assuming conditions for inference are met, the most appropriate method for answering the question of interest is (a) a one-proportion z test. (b) a one-proportion z interval. (c) a paired t test. (d) a paired t interval. (e) None of these.

Show all your work. Indicate clearly the methods you use. A software company is trying to decide whether to produce an upgrade of one of its programs. Customers would have to pay $100 for the upgrade. For the upgrade to be profitable, the company needs to sell it to more than 20% of their customers. You contact a random sample of 60 customers and find that 16 would be willing to pay$100 for the upgrade. Do the sample data give good evidence that more than 20% of the company's customers are willing to purchase the upgrade? Carry out an appropriate test at the

$$\alpha = 0.05$$

significance level.

Write a short paragraph about a sports experience you have had. Try to include a direct object in every sentence. Then, underline each direct object.

Show all your work. Indicate clearly the methods you use. "I can't get through my day without coffee" is a common statement from many students. Assumed benefits include keeping students awake during lectures and making them more alert for exams and tests. Students in a statistics class designed an experiment to measure memory retention with and without drinking a cup of coffee one hour before a test. This experiment took place on two different days in the same week (Monday and Wednesday). Ten students were used. Each student received no coffee or one cup of coffee one hour before the test on a particular day. The test consisted of a series of words flashed on a screen, after which the student had to write down as many of the words as possible. On the other day, each student received a different amount of coffee (none or one cup). One of the researchers suggested that all the subjects in the experiment drink no coffee before Monday's test and one cup of coffee before Wednesday's test. Explain to the researcher why this is a bad idea and suggest a better method of deciding when each subject receives the two treatments.

What is the sticker price? Sports car. Base price is $17,495. Options: Anti-lock brakes for$500. Automatic transmission for $995. Destination charge is$400.

In 2005, the average car in the United States was driven 12.4 thousand miles, as reported by the Federal Highway Administration in Highway Statistics. On the WeissStats CD, we provide last year’s distance driven, in thousands of miles, by each of 500 randomly selected cars. Use the technology of your choice to do the following. a. Obtain a normal probability plot and histogram of the data. b. Based on your results from part (a), can you reasonably apply the one-mean t-test to the data? Explain your reasoning. c. At the 5% significance level, do the data provide sufficient evidence to conclude that the mean distance driven last year differs from that in 2005?

Select the best answer. An SRS of 100 postal employees found that the average time these employees had worked at the postal service was 7 years with standard deviation 2 years. Do these data provide convincing evidence that the mean time of employment

$$\mu$$

for the population of postal employees has changed from the value of 7.5 that was true 20 years ago? To determine this, we test the hypotheses

$$H_0: \mu = 7.5$$

versus

$$H_a: \mu \neq 7.5$$

using a one-sample t test. What conclusion should we draw at the 5% significance level? (a) There is convincing evidence that the mean time working with the postal service has changed. (b) There is not convincing evidence that the mean time working with the postal service has changed. (c) There is convincing evidence that the mean time working with the postal service is still 7.5 years. (d) There is convincing evidence that the mean time working with the postal service is now 7 years. (e) We cannot draw a conclusion at the 5% significance level. The sample size is too small.

If $X \sim N(2,9),$ compute a. $P(X \geq 2)$ b. $P(1 \leq X<7)$ c. $P(-2.5 \leq X<-1)$ d. $P(-3 \leq X-2<3)$

Suppose that the sample mean was calculated as 500. Estimate the population mean with 95% confidence.

Select the best answer. A researcher claims to have found a drug that causes people to grow taller. The coach of the basketball team at Brandon University has expressed interest but demands evidence. Over 1000 Brandon students volunteer to participate in an experiment to test this new drug. Fifty of the volunteers are randomly selected, their heights are measured, and they are given the drug. Two weeks later, their heights are measured again. The power of the test to detect an average increase in height of 1 inch could be increased by (a) using only volunteers from the basketball team in the experiment. (b) using

$$\alpha = 0.01$$

instead of

$$\alpha = 0.05.$$

(c) using

$$\alpha = 0.05$$

instead of

$$\alpha = 0.01.$$

(d) giving the drug to 25 randomly selected students instead of 50. (e) using a two-sided test instead of a one-sided test.

A drug company has developed a new vaccine for preventing the flu. The company claims that fewer than 5% of adults who use its vaccine will get the flu. To test the claim, researchers give the vaccine to a random sample of 1000 adults. Of these, 43 get the flu. Do these data provide convincing evidence to support the company's claim?