Exam 9: Hypothesis Testing

We are testing H₀: µ ≤ 42;versus H_A: µ > 42.When = 45,s = 1.2,and n = 15,at α = .01 we do not reject the null hypothesis.(Assume that the population from which the sample is selected is normally distributed. )

If a one-sided null hypothesis for a single mean cannot be 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.

For the following hypothesis test,where H₀: μ ≤ 10;vs.H_A: μ > 10,we reject H₀ at level of significance α and conclude that the true mean is greater than 10,when the true mean is really 8.Based on this information,we can state that we have:

The value of χ²_α in a particular situation depends on:

A(n)_____________ hypothesis is the statement that is being tested.It usually represents the status quo,and it is not rejected unless there is convincing sample evidence that it is false.

A null hypothesis is not rejected at a given level of significance.As the assumed value of the mean gets further away from the true population mean,the type II error will _____________.

Determine the p-value for H₀: p = .5;versus H_A: p ≠ .5,when n = 225 and = .54.

The level of significance α indicates the probability of rejecting a false null hypothesis.

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.The alternative hypothesis can be written as H_A: μ > 100.(Assume the population is normally distributed. )

A baker must monitor the temperature at which cookies are baked.Too much variation will cause inconsistency in the texture of the cookies.Past records show that the variance of the temperatures has been 1.44 degrees.A random sample of 30 batches of cookies is selected,and the sample variance of the temperature is 4.41 degrees.Test the hypothesis that the temperature variance has increased above 1.44 degrees at α = .05.

We are testing H₀: μ ≥ 2.5;versus H_A: μ < 2.5.When = 2.46,s = .05,and n = 26,at α = .10 we reject the null hypothesis.(Assume that the population from which the sample is selected is normally distributed. )

A Type II error is failing to reject a false null hypothesis.

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 population standard deviation was 1.1 minutes.Calculate the p-value that corresponds to the test statistic.

A survey of the wine market has shown that the preferred wine for 17 percent of Americans is merlot.A wine producer in California,where merlot is produced,believes the figure is higher in California.She contacts a random sample of 550 California residents and asks which wine they purchase most often.Suppose 115 replied that merlot was the primary wine.Calculate the appropriate test statistic to test the hypotheses.

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 = 14.2 minutes.What is the critical value for α = .05 to test the hypotheses and conduct a test to determine if the null hypothesis can be rejected.

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 the p-value and determine if the process is working properly when testing at α = .10.

A baker must monitor the temperature at which cookies are baked.Too much variation will cause inconsistency in the texture of the cookies.Past records show that the variance of the temperatures has been 1.44 degrees.A random sample of 30 batches of cookies is selected,and the sample variance of the temperature is 4.41 degrees.What is the 95 percent confidence interval for σ² at α = .05?

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.Test the hypotheses at α = .05.

A baker must monitor the temperature at which cookies are baked.Too much variation will cause inconsistency in the texture of the cookies.Past records show that the variance of the temperatures has been 1.44 degrees.A random sample of 30 batches of cookies is selected,and the sample variance of the temperature is 4.41 degrees.What is the test statistic for testing the null hypothesis that the population variance has increased above 1.44 degrees?

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 population standard deviation was 1.1 minutes.Calculate the appropriate test statistic to test the hypotheses.