Exam 9: Hypothesis Testing

If a two-sided null hypothesis cannot be rejected for a single mean at a given significance level,then the corresponding one-sided null hypothesis (i.e. ,the same sample size,the same standard deviation,and the same mean)will ______________ be rejected at the same significance level.

When testing a hypothesis about a single mean,if the sample size is 20,the population standard deviation is unknown,and the population is assumed to be a normal distribution,the correct test statistic to use is ___________.

We are testing H₀: μ ≤ .95;versus H_A: μ > .95.When = .99,s = .12,and n = 24,at alpha = .05,we reject H₀.(Assume a normally distributed population. )

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.

In a bottling process,a manufacturer will lose money if the bottles contain either more or less than is claimed on the label.Suppose a quality manager for a steak sauce company is interested in testing whether the mean number of ounces of steak sauce per restaurant-size bottle differs from the labeled amount of 20 ounces.The manager samples nine bottles,measures their contents,and finds the sample mean is 19.7 ounces and the sample standard deviation is 0.3 ounces.Calculate the appropriate test statistic to test the hypotheses.

Consider an engine parts supplier,and suppose the supplier has determined that the mean and variance of the population of all cylindrical engine part outside diameters produced by the current machine are,respectively,2.5 inches and .00075.To reduce this variance,a new machine is designed.A random sample of 20 outside diameters produced by this new machine has a sample mean of 2.5 inches and a variance of s² = .0002 (normal distribution).In order for a cylindrical engine part to give an engine long life,the outside diameter must be between 2.43 and 2.57 inches.Using the upper end of the 95 percent confidence interval for σ and assuming that μ = 2.5,determine whether 99.73 percent of the outside diameters produced by the new machine are within the specification limits.

Last year,during an investigation of the time spent reading emails on a daily basis,researchers found that on Monday the average time was 50 minutes.Office workers claim that with the increased spam and junk mail,this time has now increased.To conduct a test,a sample of 25 employees is selected,with the following results: sample mean = 51.05 minutes and sample standard deviation = 4.42 minutes.Calculate the appropriate test statistic to test the hypothesis that the time has increased from last year.

The manager of a grocery store wants to determine whether the amount of water contained in 1-gallon bottles purchased from a nationally known manufacturer actually average 1 gallon.It is known from the 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 bottle is found to be 0.995 gallon.Calculate a confidence interval to test the hypotheses at α = .001.

Assuming that the null hypothesis is true,the ______________ is the probability of observing a value of the test statistic that is at least as extreme as the value actually computed from the sample data.

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 α = .05,we do not reject H₀.

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 percent 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 United States indicates that 147 are in default.Calculate the p-value associated with the test statistic,and test the hypothesis that the default rate for the selected region is lower than the national percentage at α = .01.

If you live in California,the decision to buy earthquake insurance is an important one.A survey revealed that only 133 of 337 randomly selected residences in one California county were protected by earthquake insurance.What is the p-value associated with the test statistic calculated to test the claim that less than 40 percent of the county residents are protected by earthquake insurance?

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 whether 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.One way of expressing the null hypothesis is H₀: μ = 100.

The power of a statistical test is the probability of rejecting the null hypothesis when it is false.

According to a national survey,the average commuting time for people who commute to a city with a population of 1 to 3 million is 19.0 minutes.Suppose a researcher lives in a city with a population of 2.4 million and wants to test this claim in her city.Taking a random sample of 20 commuters,she calculates a mean time of 19.346 minutes and a standard deviation of 2.842 minutes.Test the hypotheses at α = .10.

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 population standard deviation is assumed to be 1.3 days.What is the critical value for α = .001 to test the claim that μ is greater than 7.5 days?

A sample of 400 journalism majors at a major research university was asked if they agreed with the following statement: Government should be more involved in oversight and regulation of reporting. Fifty-two percent of the respondents agreed with the statement.Calculate the appropriate test statistic to test the claim that at least 50 percent of journalism majors agree with the statement.

Standard X-ray machines should give radiation dosages below 5.00 milliroentgens.To test a certain X-ray machine,a sample of 36 observations is taken,with a mean of 4.13 mR and a population standard deviation of 1.91 mR.Calculate the appropriate test statistic to test the hypotheses.

In a sample of n = 16 selected from a normally distributed population,we find a population standard deviation of s = 10.What is the value of χ² if we are testing H₀: σ² = 144?

χ²_α is the point on the vertical axis under the curve of the chi-square distribution that gives a right-hand tail area equal to α.