Exam 9: Hypothesis Testing

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.

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 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 bottle is found to be 0.995 gallon.Calculate the p-value and test whether the manufacturer's specifications are being met at α = .001.

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 800 pounds per square inch.The calculated z test statistic is a positive value that leads to a p-value of .045 for the test.If the significance level (α)is .05,the null hypothesis would be rejected.

We are testing H₀: ? ? .95;versus H_A: ? > .95.When $\bar { X } = .99$ s = .12,and n = 24,at alpha = .05,we reject H₀.(Assume a normally distributed population. )

Determine the p-value for H₀: μ = 95;versus H_A: μ ≠ 95,when $\bar { X }$

Assuming a fixed sample size,as α (Type I error)decreases,β (Type II error)___________.

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.

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 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 bottle is found to be 0.995 gallon.Calculate the test statistic.

A company has developed a new ink-jet cartridge for its printer that it believes has a longer lifetime on average than the one currently being produced.To investigate its length of life,40 of the new cartridges were tested by counting the number of high-quality printed pages each was able to produce.The sample mean and standard deviation were determined to be 1511.4 pages and 35.7 pages,respectively.The historical average lifetime for cartridges produced by the current process is 1502.5 pages.Calculate the appropriate test statistic to test the hypotheses.

It has been hypothesized that on average employees spend one hour a day playing video games at work.To test this at her company,a manager takes a random sample of 35 employees,who showed a mean time of 55 minutes per day with an assumed population standard deviation of 5 minutes.Calculate a confidence interval to test the hypotheses that the employees spend a different amount of time from one hour (60 minutes)at α = .02 and interpret.

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 the test statistic to test these hypotheses.

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.What is the critical value for testing these hypotheses at α = .001.

It is estimated that the average person in the United States uses 123 gallons of water per day.Some environmentalists believe this figure is too high and conduct a survey of 40 randomly selected Americans.They find a mean of 113.03 gallons and a population standard deviation of 25.99 gallons.Calculate the appropriate test statistic to test the hypotheses.

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.

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 the test statistic for testing that the number of tablets is significantly different from 60.

A mail-order business prides itself in its ability to fill customers' orders in less than six calendar days,on average.Periodically,the operations manager selects a random sample of customer orders and determines the number of days required to fill the orders.On one occasion when a sample of 39 orders was selected,the average number of days was 6.65 with a population standard deviation of 1.5 days.What is the critical value for α = .10 to test the hypotheses.

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.

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

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 = .01,we can reject 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 ___________.