Exam 9: Introduction to Hypothesis Testing

A cell phone manufacturer claims that its phone will last for more than 8 hours of continuous talk time when the battery is fully charged.To test this claim a sample of n = 18 phones were tested.The results showed a sample mean of 8.2 hours and a sample standard deviation of 0.4 hour.Conduct the hypothesis test using a 0.5 level of significance and determine whether or not the company's claim is supported.

A major package delivery company claims that at least 95 percent of the packages it delivers reach the destination on time.As part of the evidence in a lawsuit against the package company,a random sample of n = 200 packages was selected.A total of 188 of these packages were delivered on time.Using a significance level of .05,the test statistic for this test is approximately z = -0.65.

Nationwide Mutual Insurance,based in Columbus,Ohio,is one of the largest diversified insurance and financial services organizations in the world,with more than $157 billion in assets.Nationwide ranked 108th on the Fortune 100 list in 2008.The company provides a full range of insurance and financial services.In a recent news release Nationwide reported the results of a new survey of 1,097 identity theft victims.The survey shows victims spend an average of 81 hours trying to resolve their cases.If the true average time spent was 81 hours,determine the probability that a test of hypothesis designed to test that the average was less than 85 hours would reject the research hypothesis.Use α= 0.05 and a standard deviation of 50.

Hono Golf is a manufacturer of golf products in Taiwan and China.One of the golf accessories it produces at its plant in Tainan Hsing,Taiwan,is plastic golf tees.The injector molder produces golf tees that are designed to have an average height of 66 mm.To determine if this specification is met,random samples are taken from the production floor.One sample is contained in the file labeled THeight.Determine if the process is not producing the tees to specification.Use a significance level of 0.01.

When deciding the null and alternative hypotheses,the rule of thumb is that if the claim contains the equality (e.g. ,at least,at most,no different from,etc. ),the claim becomes the null hypothesis.If the claim does not contain the equality (e.g. ,less than,more than,different from),the claim is the alternative hypothesis.

Lube-Tech is a major chain whose primary business is performing lube and oil changes for passenger vehicles.The national operations manager has stated in an industry newsletter that the mean number of miles between oil changes for all passenger cars exceeds 4,200 miles.To test this,an industry group has selected a random sample of 100 vehicles that have come into a lube shop and determined the number of miles since the last oil change and lube.The sample mean was 4,278 and the sample standard deviation was 780 miles.Based on this information,the test statistic is approximately t = 1.000.

A one-tailed hypothesis for a population mean with a significance level equal to .05 will have a critical value equal to z = .45.

A house cleaning service claims that it can clean a four bedroom house in less than 2 hours.A sample of n = 16 houses is taken and the sample mean is found to be 1.97 hours and the sample standard deviation is found to be 0.1 hours.Using a 0.05 level of significance the correct conclusion is:

A concern of Major League Baseball is that games last too long.Some executives in the league's headquarters believe that the mean length of games this past year exceeded 3 hours (180 minutes).To test this,the league selected a random sample of 80 games and found the following results: = 193 minutes and s = 16 minutes. Based on these results,if the null hypothesis is tested using an alpha level equal to 0.10,which of the following is true?

Woof Chow Dog Food Company believes that it has a market share of 25 percent.It surveys n = 100 dog owners and ask whether or not Woof Chow is their regular brand of dog food,and 23 people say yes.Based upon this information,what is the critical value if the hypothesis is to be tested at the 0.05 level of significance?

Aceco has a contract with a supplier to ship parts that contain no more than three percent defects.When a large shipment of parts comes in,Aceco samples n = 150.Based on the results of the sample,they either accept the shipment or reject it.If Aceco wants no more than a 0.10 chance of rejecting a good shipment,the cut-off between accepting and rejecting should be 0.0478 or 4.78 percent of the sample.

An issue that faces individuals investing for retirement is allocating assets among different investment choices.Suppose a study conducted 10 years ago showed that 65% of investors preferred stocks to real estate as an investment.In a recent random sample of 900 investors,540 preferred real estate to stocks.Is this new data sufficient to allow you to conclude that the proportion of investors preferring stocks to real estate has declined from 10 years ago? Conduct your analysis at the α = 0.02 level of significance.

What is meant by the terms Type I and Type II statistical error?

For the following hypothesis test With n = 100 and p = 0.66,state the decision rule in terms of the critical value of the test statistic

If we are performing a two-tailed test of whether μ = 100,the probability of detecting a shift of the mean to 105 will be ________ the probability of detecting a shift of the mean to 110.

A company that makes and markets a device that is aimed at helping people quit smoking claims that at least 70 percent of the people who have used the product have quit smoking.To test this,a random sample of n = 100 product users was selected.The critical value for the hypothesis test using a significance level of 0.05 would be approximately -1.645.

In a one-tailed hypothesis test,the larger the significance level,the greater the critical value will be.

Woof Chow Dog Food Company believes that it has a market share of 25 percent.It surveys n = 100 dog owners and ask whether or not Woof Chow is their regular brand of dog food,and 23 people say yes.Based upon this information,what is the value of the test statistic?

A major airline has stated in an industry report that its mean onground time between domestic flights is less than 18 minutes.To test this,the company plans to sample 36 randomly selected flights and use a significance level of .10.Assuming that the population standard deviation is known to be 4.0 minutes,if the true population mean is 16 minutes,the decision maker could end up making either a Type I or a Type II error depending on the sample result.

Suppose we want to test H₀ : μ ≥ 30 versus H₁ : μ < 30.Which of the following possible sample results based on a sample of size 36 gives the strongest evidence to reject H₀ in favor of H₁?