Exam 18: Testing Hypotheses

A mayor is concerned about the percentage of city residents who express disapproval of his job performance. His political committee pays for a newspaper ad, hoping that it will keep the disapproval rate below $12 \%$ . They will use a follow-up poll to assess the ad's effectiveness. The correct null and alternative hypotheses for testing this polls effectiveness are

The manufacturer of a refrigerator system produces refrigerators that are supposed to maintain a true mean temperature, μ, of 48°F, ideal for certain beverages.The owner of a Beverage company does not agree with the refrigerator manufacturer, and will conduct a Hypothesis test to determine whether the true mean temperature differs from this value.

Using the t-tables, software, or a calculator, estimate the critical value of t for the given confidence interval and degrees of freedom: 99% confidence interval with df = 24

In the past, the mean running time for a certain type of flashlight battery has been 8.5 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 changed as a result.

$5 \%$ of trucks of a certain model have needed new engines after being driven between 0 and 100 miles. The manufacturer hopes that the redesign of one of the engine's components has solved this problem. The correct null and alternative hypotheses for testing this redesign are

The owner of a football team claims that the average attendance at games is over 74,900, and he is therefore justified in moving the team to a city with a larger stadium.An independent Investigator will conduct a hypothesis test to determine whether his claim is accurate.

A skeptical paranormal researcher claims that the proportion of Americans that have seen a UFO is less than $5 \%$ . The correct null and alternative hypotheses for testing this claim are

A manufacturer claims that the mean amount of juice in its 16 ounce bottles are 16.1 ounces. A consumer advocacy group wants to perform a hypothesis test to determine whether the Mean amount is actually less than this.

Use the $t$ -tables, software, or a calculator to estimate the indicated $P$ -value: $P$ -value for $t \geq 1.76$ with 17 degrees of freedom

An entomologist writes an article in a scientific journal which claims that fewer than $17 \%$ of male fireflies are unable to produce light due to a genetic mutation. The correct null and alternative hypotheses for testing this claim are

A pharmaceutical company wants to answer the question whether it takes longer than 45 seconds for a drug in pill form to dissolve in the gastric juices of the stomach. A sample was taken from patients taking the given drug in pill form and times for the pills to be dissolved were measured. State assumptions of the test. I. The subjects must be part of a medical study group investigating the drug. II. The subjects in the sample must be randomly selected from a population. III. The sample data must come from a normally distributed population of observations for the variable under study.

Data in 1980 showed that about 40% of the adult population had never smoked cigarettes.In 2004, a national health survey interviewed a random sample of 2000 adults and found that 50% had never been smokers.Create a 95% confidence interval for the proportion of adults (in 2004) who had never been smokers.

A company hopes to improve its engines, setting a goal of no more than $3 \%$ of customers using their warranty on defective engine parts. A random survey of 1400 customers found only 30 with complaints. Create a $95 \%$ confidence interval for the true level of warranty users among all customers.

A report on the U.S. economy indicates that $28 \%$ of Americans have experienced difficulty in making mortgage payments. A news organization randomly sampled 400 Americans from 10 cities named the "fastest dying cities in the U.S." (Forbes Magazine, August 2008) and found that 136 reported such difficulty. Does this indicate that the problem is more severe among these cities? The correct null and alternative hypotheses for testing this claim are

A statistician consulting for a state department of transportation conducts a study to see if the proportion of drivers who are intoxicated has decreased since last year. $H _ { 0 }$ : The proportion is the same as last year $H _ { A }$ : The proportion is less than last year. The $P$ -value of a significance test is greater than the significance level. She can conclude:

Use the $t$ -tables, software, or a calculator to estimate the indicated $P$ -value: $P$ -value for $t \geq - 1.47$ with 21 degrees of freedom

A report on the U.S. economy indicates that $28 \%$ of Americans have experienced difficulty in making mortgage payments. A news organization randomly sampled 400 Americans from 10 cities named the "fastest dying cities in the U.S." (Forbes Magazine, August 2008) and found that 136 reported such difficulty. Does this indicate that the problem is more severe among these cities? The correct value of the test statistic for testing this claim is