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.

Alpha (α)is the probability that the test statistic would assume a value at or more extreme than the observed value of the test.

Using the p-value rule for a population proportion or mean,if the level of significance is less than the p-value,the null hypothesis is rejected.

Using the p-value rule,if a null hypothesis is not rejected at a significance level of .05,it will _____________ be rejected at a significance level of .01

The HR department tested how long employees stay with the company in their current positions.A random sample of 50 employees yielded a mean of 2.79 years and σ = .76.The sample evidence indicates that the average time is less than 3 years and is significant at α = .01.

When we test H₀: p = .2;versus H_A: p ≠.2,with = .26 and n = 100,at alpha = .05,we reject the null hypothesis.

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 whether there is enough evidence to establish that the average weight for the population of product X is greater than 100 lb.Assume the population is normally distributed.Therefore,one way of expressing the null hypothesis is H₀: μ = 100.

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. )

For a given hypothesis test,if we do not reject H₀,and H₀ is true,

We are testing H₀: p ≥ .7;versus H_A: p < .7.With = .63 and n = 100,at α = .01,we do not reject the null hypothesis.

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 a confidence interval to test the hypotheses at α = .001 and determine whether the specifications are being met.

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

Using either the critical value rule or the p-value rule,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.

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 and determine if the process should be stopped.

To compute a 95 percent confidence interval for σ²,we use n − 1 degrees of freedom and the chi-square points on the distribution curve of χ²_α/2 and of χ²_1−(α/2).

We are testing H₀: μ = 32;versus H_A: μ > 32.If = 36,s = 1.6,and n = 30,at α = .05,we should reject H₀.

Rejecting a true null hypothesis is called a ______________ error.

It can be established at α = .05 that a majority of students favor the plus/minus grading system at a university if in a random sample of 500 students,270 favor the system.

For a fixed sample size,the lower we set α,the higher is the ___________.

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.Using the critical value rule,at α = .05,we would reject the null hypothesis.