Exam 9: Hypothesis Testing

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 1500 voting age citizens.1020 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 failing to reject a false null hypothesis.

In a study of distances traveled by buses before the first major engine failure,a sample of 191 buses results in a mean of 96,700 miles and a population standard deviation of 37,500 miles.Calculate the p-value corresponding to the test statistic used to test the claim that the mean distance traveled before a major engine failure is more than 90,000 miles,and determine if the null hypothesis can be rejected at α = .01.

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.What is the critical value for α = .001 to test the claim that μ is greater than 7.5 days.

When we test H₀: p = .2;versus H_A: p ?.2,with $\hat { p } = .26$ and n = 100,at alpha = .05,we reject the null hypothesis.

Last year,KAAA's share of the 6 p.m.news audience was approximately equal to,but not greater than,25 percent.The station's advertising department believes the current audience share is higher than last year's 25 percent share.In an attempt to substantiate this belief,the station surveyed a random sample of 400 viewers of 6 p.m.news and found that 146 watched KAAA.Calculate the appropriate test statistic to test the hypotheses.

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 1500 voting age citizens.1020 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.What is the p-value for this test?

In research on cell phone use by teenagers,it was found that the average connect time for a call was at least 15 minutes.Social psychologists feel that this study understated the time.To determine this claim,cell phone bills for 15 teenagers were evaluated.On average,the time spent was 18.5 minutes,with a sample standard deviation of 4 minutes.(Assume a normal distribution. )Calculate the appropriate test statistic to test the hypotheses.

The university registrar claims that fewer than 20 percent of the students who enroll at Ivy University graduate in four years.To test this claim,a random sample of 100 students was selected,and 18 were found to have graduated in four years.Calculate the appropriate test statistic to test the hypotheses.

If you live in California,the decision to buy earthquake insurance is an important one.A survey revealed that only 133 of 337 randomly selected residences in one California county were protected by earthquake insurance.Calculate the appropriate test statistic to test the claim that less than 40 percent of the residents in the county are protected by earthquake insurance.

As the Type II error β of statistical test increases,the power of the test _____________.

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.

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.What is the critical value used to test the claim at α = .05?

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 a confidence interval to test the hypotheses at α = .10.

When testing a hypothesis about a single mean,if the sample size is 20,the population standard deviation is unknown,and the population is assumed to be a normal distribution,the correct test statistic to use is ___________.

When conducting a hypothesis test about a single mean,other relevant factors held constant,increasing the level of significance α from .05 to .10 will reduce the probability of a Type II error.

When the null hypothesis is not rejected,there is no possibility of making a Type I error.

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.

Standard X-ray machines should give radiation dosages below 5.00 milliroentgens.To test a certain X-ray machine,a sample of 36 observations is taken,with a mean of 4.13 mR and a population standard deviation of 1.91 mR.Calculate the appropriate test statistic to test the hypotheses.

Standard X-ray machines should give radiation dosages below 5.00 milliroentgens.To test a certain X-ray machine,a sample of 36 observations is taken,with a mean of 4.13 mR and a population standard deviation of 1.91 mR.Calculate the p-value for this test statistic and test the claim at α = .05.