Exam 9: Hypothesis Testing

An airline claims that the no-show rate for passengers booked on its flights is less than 6%. Of 380 randomly selected reservations, 18 were no-shows. Use Table 5.1 to find the best estimate of the P- value for a test of the airline's claim.

A study of a brand of "in the shell peanuts" gives the following results: Number of Peanuts per bag Probability 25 0.006 30 0.020 35 0.093 40 0.150 45 0.350 50 0.217 55 0.170 If a fan purchased a bag with 30 peanuts, what is the lowest level at which this would be a significant event?

According to a recent poll 53% of Americans would vote for the incumbent president. If a random sample of 100 people results in 45% who would vote for the incumbent, test the hypothesis that the actual percentage is 53%. Use a 0.10 significance level and a two-tailed test.

A two-tailed test is conducted at the 5% significance level. What is the right tail percentile required to reject the null hypothesis?

The manufacturer of a refrigerator system for beer kegs produces refrigerators that are supposed to maintain a true mean temperature, µ, of 46ºF, ideal for a certain type of German pilsner. The owner of the brewery does not agree with the refrigerator manufacturer, and claims he can prove that the true mean temperature is incorrect. Assuming that a hypothesis test of the claim has been conducted and that the conclusion is to reject the null hypothesis, state the conclusion in non-technical terms.

A health insurer has determined that the "reasonable and customary" fee for a certain medical procedure is $1200. They suspect that the average fee charged by one particular clinic for this procedure is higher than $1200. The insurer wants to perform a hypothesis test to determine whether their suspicion is correct. The mean fee charged by the clinic for a random sample of 65 patients receiving this procedure was $1280. Do the data provide sufficient evidence to conclude that the mean fee charged by this particular clinic is higher than $1200? Perform the appropriate hypothesis test using a significance level of 0.01. Assume that ? = $220.

A manufacturer wishes to test the claim that one of its pancake mixes has a mean weight that does not equal 24 ounces as advertised. Determine the conclusion of the hypothesis test assuming that the results of the sampling lead to rejection of the null hypothesis.

A nationwide study of American homeowners revealed that 65% have one or more lawn mowers. A lawn equipment manufacturer, located in Omaha, feels the estimate is too low for households in omaha. Find the P-value for a test of the claim that the proportion with lawn mowers in Omaha is higher than 65%. Among 497 randomly selected homes in Omaha, 340 had one or more lawn Mowers. Use Table 5.1 to find the best answer.

A study of a brand of "in the shell peanuts" gives the following results: Number of Peanuts per bag Probability 25 0.003 30 0.020 35 0.090 40 0.150 45 0.350 50 0.217 55 0.170 A significant event at the 0.01 level is a fan getting a bag with how many peanuts?

$\mathrm{H}_{\mathrm{a}}: \mu>19, \bar{x}=23.8, \sigma=8, \mathrm{n}=100$ ; without computing a $\mathrm{P}$ -value, determine whether the alternate hypothesis is supported and give a reason for your conclusion.

A long-distance telephone company claims that the mean duration of long-distance telephone calls originating in one town was greater than 9.4 minutes, which is the average for the state. Determine the conclusion of the hypothesis test assuming that the results of the sampling do not lead to rejection of the null hypothesis.

A cereal company claims that the mean weight of the cereal in its 14 oz. packets is at least 14 oz. Assume that a hypothesis test of the claim has been conducted and that the conclusion of the test was to reject the null hypothesis. Identify the population to which the results of the test apply.

In 1990, the average math SAT score for students at one school was 495. Five years later, a teacher wants to perform a hypothesis test to determine whether the average SAT score of students at the School has changed from the 1990 mean of 495. The hypotheses are: :\mu=495 :\mu495 Explain the meaning of a Type II error.

A consumer advocacy group claims that the mean amount of juice in a 16 ounce bottled drink is not 16 ounces, as stated by the bottler. Determine the null and alternative hypotheses for the test Described.

A poll of 1068 adult Americans reveals that 52% of the voters surveyed prefer the Democratic candidate for the presidency. At the 0.05 significance level, test the claim that more than half of all voters prefer the Democrat.

In the past, the mean running time for a certain type of flashlight battery has been 9.8 hours. The manufacturer has introduced a change in the production method and wants to perform a hypothesis test to determine whether the mean running time has increased as a result. The hypotheses are: $\mathrm { H } _ { 0 } : \mu = 9.8$ hours $\mathrm { H } _ { \mathrm { a } } : \mu > 9.8 \text { hours }$ Suppose that the results of the sampling lead to rejection of the null hypothesis. Classify that conclusion as a Type I error, a Type II error, or a correct decision, if in fact the mean running time has not increased.

In 1990, the average duration of long-distance telephone calls originating in one town was 9.3 minutes. A long-distance telephone company wants to perform a hypothesis test to determine whether the average duration of long-distance phone calls has changed from the 1990 mean of 9.3 minutes. Formulate the null and alternative hypotheses for the study described.

The average diastolic blood pressure of a group of men suffering from high blood pressure is 96 mmHg. During a clinical trial, the men receive a medication, which it is hoped, will lower their blood pressure. After three months, the researcher wants to perform a hypothesis test to determine whether the average diastolic blood pressure of the men has decreased. The hypotheses are: :\mu=96 :\mu<96 Explain the meaning of a Type II error.

A two-tailed test is conducted at the 5% significance level. What is the P-value required to reject the null hypothesis?

The owner of a football team claims that the average attendance at home games is over 3000, and he is therefore justified in moving the team to a city with a larger stadium. Assuming that a hypothesis test of the claim has been conducted and that the conclusion is failure to reject the null hypothesis, State the conclusion in non-technical terms.