Exam 9: Hypothesis Testing

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 _____________.

As the level of significance,α,increases,we are more likely to reject the null hypothesis.

When applying either the critical value rule or the p-value rule about a single mean,reducing the level of significance (α)will increase the size of the rejection region.

Using the critical value rule,if a two-sided null hypothesis cannot be rejected for a single mean at a given significance level,then 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.

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

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

A Type I error is rejecting a true null hypothesis.

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.

The exact shape of the chi-square distribution depends on the degrees of freedom.

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.

We test H₀: μ ≤ 3.0;versus H_A: μ > 3.0.If = 3.44,s = .57,and n = 13,at a significance level of .05,we do not reject H₀.(Assume population normality. )

When testing a hypothesis about a single mean,a sample size of 200 is selected from a normally distributed population.If the population standard deviation is known,the correct test statistic to use is ___________.

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.

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.

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.Using the critical value rule,at α = .01,we can reject the null hypothesis.

The value of the test statistic is compared with a(n)_______________ in order to decide whether the null hypothesis can be rejected.

Everything else being constant,increasing the sample size decreases the probability of committing a Type II error.

When evaluating a new process,using the square root of the upper end of the confidence interval for σ² gives an estimate of the smallest that σ for the new process might reasonably be.

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.Historically,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 using the critical value rule,we can show that the completion time has increased.

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. )