Exam 9: Hypothesis Testing

In 1930,the average size of a public restroom was 172 square feet.By 1990,due to federal disability laws,the average size had increased to 471 square feet.Suppose that a design team believes that this standard has increased from the 1990 level.They randomly sample 23 public restrooms in a major midwestern city and obtain a mean square footage of 498.78 with a standard deviation of 46.94.Test the hypotheses at α = .001.

Determine the p-value for H₀: p = .5;versus H_A: p ≠ .5,when n = 225 and V $\hat { p } = .54$

The quality control manager of a major cell phone provider is concerned about the life of the cell phone batteries they use.He took a sample of 13 batteries from a recent shipment and used them continuously until they failed to work.The manager measured the number of hours the batteries lasted and found the mean to be 550.4 with a standard deviation of 315.3.Calculate the appropriate test statistic to test the claim that the mean life of the batteries is more than 400 hours.

The quality control manager of a major cell phone provider is concerned about the life of the cell phone batteries they use.He took a sample of 13 batteries from a recent shipment and used them continuously until they failed to work.The manager measured the number of hours the batteries lasted and found the mean to be 550.4 with a standard deviation of 315.3.What is the critical value for α = .10 to test the claim that the mean life of the batteries is more than 400 hours? Test the claim at .10.

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 value of the test statistic?

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

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.At α = .05,we do not reject H₀.

For a hypothesis test about a population proportion or mean,if the level of significance is less than the p-value,the null hypothesis is rejected.

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 = 4.42 minutes.Calculate the appropriate test statistic to test the hypothesis that the time has increased from last year.

If a null hypothesis is not rejected at a significance level of .05,it will _____________ be rejected at a significance level of .01

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.

In testing H₀: p = .2;versus H_A: p ≠ .2,with $\hat { p }$ = .26 and n = 100,what is the value of the test statistic?

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.

A recent study conducted by the state government attempts to determine whether the voting public supports 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.At α = .05,we would reject the null hypothesis.

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.What is the p-value associated with the test statistic calculated to test the claim that less than 40 percent of the county residents are protected by earthquake insurance?

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.Test these hypotheses at α = .001 using the critical value.

We are testing H₀: ? ? 2.5;versus H_A: ? < 2.5.When $\bar { X } = 2.46$ s = .05,and n = 26,at ? = .10 we reject the null hypothesis.(Assume that the population from which the sample is selected is normally distributed. )

According to a national survey,the average commuting time for people who commute to a city with a population of 1 to 3 million is 19.0 minutes.Suppose a researcher lives in a city with a population of 2.4 million and wants to test this claim in her city.Taking a random sample of 20 commuters,she calculates a mean time of 19.346 minutes and a standard deviation of 2.842 minutes.Test the hypotheses at α = .10.

A mail-order business prides itself in its ability to fill customers' orders in less than six calendar days,on average.Periodically,the operations manager selects a random sample of customer orders and determines the number of days required to fill the orders.On one occasion when a sample of 39 orders was selected,the average number of days was 6.65 with a population standard deviation of 1.5 days.Calculate the appropriate test statistic to test the hypotheses.

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 I error.