Exam 9: Hypothesis Testing

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 using the p-value rule.

Based on a random sample of 25 units of product X,the average weight is 102 lb and the sample standard deviation is 10 lb.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 lb.Therefore,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.What is the 95 percent confidence interval for σ² at α = .05?

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.

When testing a null hypothesis about a single population mean and the population standard deviation is unknown,if the sample size is less than 30,one compares the computed test statistic for significance with a value from the ___________ distribution.

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 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.Find the 95 percent confidence intervals for σ² and σ for the new machine.

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

A test statistic is computed from sample data in hypothesis testing and is used in making a decision about whether or not to reject the null hypothesis.

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.If σ² denotes the variance of the population of all outside diameters that would be produced by the new machine,test H₀: σ² = .00075 versus H_a: σ² < .00075 by setting α = .05.

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 1,500 voting age citizens.1,020 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.Identify the null hypothesis.

A Type II error is defined as ________________ H₀,when it should _____________.

You cannot make a Type II error when the null hypothesis is true.

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

Using the critical value rule,if a two-sided null hypothesis is rejected for a single mean at a given significance level,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.

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

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. )

Using the p-value rule,if a null hypothesis is rejected at a significance level of .01,it will ____________ be rejected at a significance level of .05

When the null hypothesis is true,there is no possibility of making a Type I error.

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 averages 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 p-value and test whether the specifications are being met at α = .001 using the p-value rule.