Exam 9: Hypothesis Testing

In testing H₀: p ≥ .33;versus H_A: p< .33,with = .20 and n = 100,what is the value of the test statistic?

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.Assuming normality,determine whether 99.73 percent of the outside diameters produced by the current machine are within specification limits.

The larger the p-value,the more we doubt the null hypothesis.

When testing a hypothesis about a single mean,if the sample size is 51,and the population standard deviation is known,the correct test statistic to use is ___________.

A recent study conducted by the state government attempts to determine whether the voting public supports a 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.At α = .05,we would reject the null hypothesis.

The chi-square distribution is a continuous probability distribution that is skewed to the left.

A manufacturer of salad dressings uses machines to dispense liquid ingredients into bottles that move along a filling line.The machine that dispenses dressing is working properly when 8 ounces are dispensed.The standard deviation of the process is 0.15 ounces.A sample of 48 bottles is selected periodically,and the filling line is stopped if there is evidence that the mean amount dispensed is different from 8 ounces.Suppose that the mean amount dispensed in a particular sample of 48 bottles is 7.983 ounces.Calculate a confidence interval to test the hypotheses at α = .05.

Last year,TV station KAAA had a share of the 6 p.m.news audience approximately equal to,but not greater than,25 percent.The advertising department for the station believes the current audience share is higher than the 25 percent share they had last year.In an attempt to substantiate this belief,the station surveyed a random sample of 400 viewers of 6 p.m.news and found that 146 watched KAAA.Calculate the appropriate test statistic to test the hypotheses.

We are testing H₀: μ ≥ 22;versus H_A: μ < 22.Given α = .01,n = 100, = 21.431,and σ = 1.295,we should not reject H₀.

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 the test statistic.

A major car manufacturer wants to test a new catalytic converter to determine whether it meets new air pollution standards.The mean emission of all converters of this type must be less than 20 parts per million of carbon.Ten (10)converters are manufactured for testing purposes and their emission levels are measured,with a mean of 17.17 and a standard deviation of 2.98.Test the hypotheses at α = .01.

In a study of distances traveled by buses before the first major engine failure,a sample of 191 buses results in a mean of 96,700 miles and a population standard deviation of 37,500 miles.Calculate the appropriate test statistic to test the claim that the mean distance traveled before a major engine failure is more than 90,000 miles.

A microwave manufacturing company has just switched to a new automated production system.Unfortunately,the new machinery has been frequently failing and requiring repairs and service.The company has been able to provide its customers with a completion time of 6 days or less.To analyze whether the completion time has increased,the production manager took a sample of 36 jobs and found that the sample mean completion time was 6.5 days with a sample standard deviation of 1.5 days.At a significance level of .10,we can show that the completion time has increased.

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.If the claim is that the population mean is greater than 7.5 days,calculate the appropriate test statistic to test the hypotheses.

If a one-sided null hypothesis is rejected at a given significance level,then the corresponding two-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 we test H₀: p = .2;versus H_A: p ≠ .2,with = .26 and n = 100,at alpha = .05,we reject the null hypothesis.

In 1930,the average size of a public restroom was 172 square feet.By 1990,due to federal disability laws,the average size had increased to 471 square feet.Suppose that a design team believes that this standard has increased from the 1990 level.They randomly sample 23 public restrooms in a major midwestern city and obtain a mean square footage of 498.78 with a standard deviation of 46.94.Calculate the appropriate test statistic to test the hypotheses.

The local pharmacy prides itself on the accuracy of the number of tablets that are dispensed in a 60-count prescription.The new manager feels that the pharmacy assistants might have become careless in counting due to an increase in the volume of prescriptions.To test her theory,she randomly selects 40 prescriptions requiring 60 tablets and recounts the number in each bottle.She finds a sample mean of 62.05 and a standard deviation of 4.45.Calculate a confidence interval to test the hypotheses at α = .002 and interpret the result.

When conducting a hypothesis test about a single mean,other relevant factors held constant,increasing the level of significance α from .05 to .10 will reduce the probability of a Type I error.

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 p-value for this test statistic and test the claim at α = .05.