Exam 9: Hypothesis Testing

Based on a random sample of 25 units of product X,the average weight is 102 lbs. ,and the sample standard deviation is 10 lbs.We would like to decide if there is enough evidence to establish that the average weight for the population of product X is greater than 100 lbs.Assume the population is normally distributed.At $\alpha$ = .01,we can reject the null hypothesis.

A null hypothesis H₀: µ $\ge$ 2.4 is not rejected at a significance level of 0.04.( $\alpha$ = 0.04).The standard deviation for the normally distributed population is known to be 0.40.Determine the Type II error,if we assume that the actual mean is 2.125 based on a sample size of 16.

The manufacturer of an over-the-counter heartburn relief mediation claims that its product brings relief in less than 3.5 minutes,on average.To be able to make this claim the manufacturer was required by the FDA to present statistical evidence in support of the claim.The manufacturer reported that for a sample of 50 heartburn sufferers,the mean time to relief was 3.3 minutes and the standard deviation was 1.1 minutes.Calculate the p-value that corresponds to the test statistic.

One survey conducted by a major leasing company determined that the Lexus is the favorite luxury car for 25% of leases in Atlanta.Suppose a US car manufacturer conducts its own survey in an effort to determine if this figure is correct.Of the 384 leases in Atlanta surveyed,79 lease a Lexus.Calculate a confidence interval that tests the hypotheses at $\alpha$ = .02.

A Type I error is rejecting a true null hypothesis.

For the following hypothesis test where H₀: µ $\le$ 10 vs.H_a: µ > 10,we reject H₀ at level of significance $\alpha$ and conclude that the true mean is greater than 10 when the true mean is really 14.Based on this information we can state that we have:

Failure to meet payments on student loans guaranteed by the US government has been a major problem for both banks and the government.Approximately 50% of all student loans guaranteed by the government are in default.A random sample of 350 loans to college students in one region of the US indicates that 147 are in default.Calculate an interval that tests the hypotheses at $\alpha$ = .01.

The rejection of a true null hypothesis is called a ______________ error.

A cereal manufacturer is concerned that the boxes of cereal not be under filled or overfilled.Each box of cereal is supposed to contain 13 ounces of cereal.A random sample of 31 boxes is tested.The average weight is 12.58 ounces and the standard deviation is 0.25 ounces.Calculate a confidence interval to test the hypotheses at $\alpha$ = .10

As the level of significance $\alpha$ increases,we are more likely to reject the null hypothesis.

The null hypothesis is a statement that will be accepted only if there is convincing sample evidence that it is true.

A recent study conducted by the state government attempts to determine whether the voting public supports further increase in cigarette taxes.The opinion poll recently sampled 1500 voting age citizens.1020 of the sampled citizens were in favor of an increase in cigarette taxes.The state government would like to decide if there is enough evidence to establish whether the proportion of citizens supporting an increase in cigarette taxes is significantly greater than .66.The alternative hypothesis is:

A random sample of 80 companies who announced corrections to their balance sheets took a mean time of 8.1 days for the time between balance sheet construction and the complete audit.The standard deviation of these times was 1.3 days.If the claim is that the population mean is greater than 7.5 days,calculate the appropriate test statistic to test the hypotheses.

For a given hypothesis test,if we do not reject H₀,and H₀ is true.

When conducting a hypothesis test about a single mean,reducing the level of significance ( $\alpha$ )will increase the size of the rejection region.

The manager of the quality department for a tire manufacturing company wants to know the average tensile strength of rubber used in making a certain brand of radial tire.The population is normally distributed and the population standard deviation is known.She uses a Z test to test the null hypothesis that the mean tensile strength is less than or equal to 800 pounds per square inch.The calculated Z test statistic is a positive value that leads to a p-value of .067 for the test.If the significance level is .10,the null hypothesis would be rejected.

Assuming a fixed sample size,as $\alpha$ (Type I error)decreases, $\beta$ (Type II error)___________.

The manager of a grocery store wants to determine whether the amount of water contained in 1 gallon bottle purchased from a nationally known manufacturer actually average 1 gallon.It is known from the manufacturer's specifications that the standard deviation of the amount of water is equal to 0.02 gallon.A random sample of 32 bottles is selected,and the mean amount of water per 1 gallon can is found to be 0.995 gallon.Calculate a confidence interval to test the hypotheses at $\alpha$ = .001.

As the type II error $\beta$ of statistical test increases,the power of the test _____________.

A recent study conducted by the state government attempts to determine whether the voting public supports further increase in cigarette taxes.The opinion poll recently sampled 1500 voting age citizens.1020 of the sampled citizens were in favor of an increase in cigarette taxes.The state government would like to decide if there is enough evidence to establish whether the proportion of citizens supporting an increase in cigarette taxes is significantly greater than .66.Which of the following does not represent a null hypothesis?