A company is willing to renew its advertising contract with a local radio station only if the station can prove that more than 20% of the residents of the city have heard the ad and recognize the company's product. The radio station conducts a random phone survey of 400 people. a) What are the hypotheses? b) The station plan s to conduct this test using a 10% level of significance, but the company wants the significance level lowered to 5%. Why? c) What is meant by the power of this test? d) For which level of significance will the power of this test be higher? Why? e) They finally agree to use

$$\alpha = 0.05$$

, but the company proposes that the station call 600 people instead of the 400 initially proposed. Will that make the risk of Type II error higher or lower? Explain.

During routine screening, a doctor notices that 22% of her adult patients show higher than normal levels of glucose in their blood-a possible warning signal for diabetes. Hearing this, some medical researchers decide to conduct a large-scale study, hoping to estimate the proportion to within 4% with 98% confidence. How many randomly selected adults must they test.

A company is willing to renew its advertising contract with a local radio station only if the station can prove that more than $20 \%$ of the residents of the city have heard the ad and recognize the company's product. The company contacts 600 people chosen at random, and 133 can remember the ad.

c) Should the company renew the contract? Support your recommendation with an appropriate test.

A Statistics professor has observed that for several years students score an average of 105 points out of 150 on the semester exam. A sales man suggests that he try a statistics software package that gets students more involved with computers, predicting that it will increase students' scores. The software is expensive, and the salesman offers to let the professor use it for a semester to see if the scores on the final exam increase significantly. The professor will have to pay for the software only if he chooses to continue using it. a) Is this a one-tailed or two-tailed test ? Explain. b) Write the null and alternative hypotheses. c) In this context, explain what would happen if the professor makes a Type I error. d) In this context, explain what would happen if the professor make s a Type II error. e) What is meant by the power of this test?

In a drawer are two coins. They look the same, but one coin produces heads 90% of the time when spun while the other one produces heads only 30% of the time. You select one of the coins. You are allowed to spin it once and then must decide whether the coin is the 90%- or the 30%-head coin. Your null hypothesis is that your coin produces 90% heads.

What is the alternative hypothesis?

Have harsher penalties and ad campaigns increased seat-belt use among drivers and passengers? Observations of commuter traffic failed to find evidence of a significant change compared with three years ago. Explain what the study's P-value of 0.17 means in this context.

Highway safety engineers test new road signs hoping that increased reflectivity will make them more visible to drivers. Volunteers drive through a test course with several of the new- and old-style signs and rate which kind shows up the best.

Is this a one-tailed or a two-t ailed test? Why?

Students investigating the packaging of potato chip purchased 6 bags of Lay's Ruffles marked with a net weight of 28.3 grams. They carefully weighed the contents of each bag, recording the following weights (in grams): 29.3, 28.2, 29.1, 28.7, 28.9, 28.5. a) Do these data satisfy the assumptions for inference? Explain. b) Find the mean and standard deviation of the weights. c) Create a 95% confidence interval for the mean weight of such bags of chips. d) Explain in context what your interval means. e) Comment on the company's stated net weight of 28.3 grams.

Suppose you were to collect data for each pair of variables. You want to make a scatterplot. Which variable would you use as the explanatory variable and which as the response variable? Why? What would you expect to see in the scatterplot? Discuss the likely direction, form, and strength. Long-distance calls: time (minutes), cost

Bicycles arrive at a bike shop in boxes. Before they can be sold, they must be unpacked, assembled, and tuned (lubricated, adjusted, etc.). Based on past experience, the shop manager makes the following assumptions about how long this may take:

• The times for each setup phase are independent.
• The times for each phase follow a Normal model.
• The means and standard deviations of the times (in minutes) are as shown: | Phase | Mean | SD | | :--- | ---: | ---: | | Unpading | 3.5 | 0.7 | | Assembly | 21.8 | 2.4 | | Tuning | 12.3 | 2.7 |

a) What are the mean and standard deviation for the total bicycle setup time?

A company is willing to renew its advertising contract with a local radio station only if the station can prove that more than $20 \%$ of the residents of the city have heard the ad and recognize the company's product. The company contacts 600 people selected at random, and 133 can remember the ad.

b) The station plans to execute this test using a $10 \%$ level of significance, but the company wants the significance level lowered to $5 \%$. Why?

The company contacts 600 people selected at random, and only 133 remember the ad. a) Should the company renew the contract? Support your recommendation with an appropriate test. b) Explain what your P-value means in this context.

A candidate has budgeted $10,000 to spend on radio and television advertising. A radio ad costs$200 per 30-second spot, and a television ad costs $800 per 30-second spot. How many radio and television spots can the candidate purchase without exceeding the budget?

In each, (a) rewrite the statement in English without using the symbol

$$\forall$$

or

$$\exists$$

or variables and expressing your answer as simply as possible, and (b) write a negation for the statement.

$$\forall$$

colors C,

$$\exists$$

an animal A such that A is colored C.