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Exam 9: Hypothesis Testing

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Question 1

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It has been hypothesized that on average employees spend one hour a day playing video games at work.To test this at her company,a manager takes a random sample of 35 employees,who showed a mean time of 55 minutes per day with an assumed population standard deviation of 5 minutes.What is the critical value for testing these hypotheses at α = .01?

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2.326

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We are testing H₀: ? = 32;versus H_A: ? > 32.If $\overline { \mathrm { X } } = 36$ s = 1.6,and n = 30 at ? = .05,we should reject H₀.

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The local pharmacy prides itself on the accuracy of the number of tablets that are dispensed in a 60-count prescription.The new manager feels that the pharmacy assistants might have become careless in counting due to an increase in the volume of prescriptions.To test her theory,she randomly selects 40 prescriptions requiring 60 tablets and recounts the number in each bottle.She finds a sample mean of 61.35.Assume a population standard deviation of 4.45.If we have preset the probability of a Type I error equal to .05,compute the probability of a Type II error.(Assume an alternate value of the population mean of 61. )The claim is that the tablet count is different from 60.

When the null hypothesis is true,there is no possibility of making a Type I error.

In testing H₀: μ = 23;versus H_A: μ > 23,when $\bar { X }$ = 26,s = 6,and n = 20,what is the value of the test statistic?

When 100 randomly selected car owners are surveyed,it is found that the mean length of time they plan to keep their car is 7.01 years,and the population standard deviation is 3.74 years.Calculate the appropriate test statistic to test the claim that the mean for all car owners is less than 7.5 years.

For the following hypothesis test,where H₀: μ ≤ 10;vs.H_A: μ > 10,we reject H₀ at level of significance α and conclude that the true mean is greater than 10,when the true mean is really 8.Based on this information,we can state that we have:

A sample of 400 journalism majors at a major research university was asked if they agreed with the following statement: "Government should be more involved in oversight and regulation of reporting".Fifty-two percent of the respondents agreed with the statement.Calculate the appropriate test statistic to test the claim that at least 50 percent of journalism majors agree with the statement.

The HR department tested how long employees stays 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.

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 whether 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.One way of expressing the null hypothesis is H₀: μ = 100.

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 four minutes.(Assume a normal distribution. )What is the critical value for α = .001 to test the hypotheses.Determine whether the null hypothesis can be rejected at this 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 whether 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 value of the test statistic to test the claim?

Determine the p-value for H₀: μ ≥ 95;versus H_A: μ < 95,when $\bar { X } = 90.2$

In testing H₀: μ ≤ 23;versus H_A: μ > 23,when $\bar { X }$ = 26,σ = 6,and n = 30,what is the value of the test statistic?

After testing H₀: p = .33;versus H_A: p < .33;at ? = .05,with $\hat { p } = .20$ and n = 100,we do not reject H₀.

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 the p-value and determine if the process is working properly when testing at α = .10.

Failure to meet payments on student loans guaranteed by the US government has been a major problem for both banks and the government.Approximately 50 percent of all student loans guaranteed by the government are in default.A random sample of 350 loans to college students in one region of the United States indicates that 147 are in default.Calculate the appropriate test statistic to test the hypothesis that the selected region's default rate is lower than the national percentage.

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 _____________.

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

You cannot make a Type II error when the null hypothesis is true.