Exam 9: Hypothesis Testing

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 sample value of the test statistic?

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% 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 US indicates that 147 are in default.Calculate the appropriate test statistic to test the hypotheses.

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 $\alpha$ = .10 to test the claim that the mean life of the batteries is more than 400 hours.

The manager of a local specialty store is concerned with a possible slowdown in payments by her customers.She measures the rate of payment in terms of the average number of days receivables are outstanding.Generally,the store has maintained an average of 50 days with a standard deviation of 10 days.A random sample of 25 accounts gives an average of 54 days outstanding with a standard deviation of 8 days.What is the critical value for $\alpha$ = .01 to test the hypotheses.

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 62.05 and a standard deviation of 4.45.Calculate the test statistic.

Determine the p-value for H₀: µ $\ge$ 95 versus H_A: µ < 95 when = 90.2,s = 9.92,and n = 37.

Determine the p-value for H₀: µ = 95 versus H_A: µ $\neq$ 95 when = 90.2,s = 9.92,and n = 37.

In testing H₀: p = .2 versus H_A: p $\neq$ .2 with = .26 and n = 100,what is the value of the z-statistic?

A Type II error is failing to reject a false null hypothesis.

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

After testing at = .05 H₀: p = .33 versus H_A: p < .33 with = .20 and n = 100,we fail to reject H₀.

Type II error is defined as the probability of ________________ H₀,when it should ___________.

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.

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.Calculate the appropriate test statistic to test the hypotheses.

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.Calculate the appropriate test statistic to test the hypotheses.

In testing H₀: µ = 23 versus H_A: µ > 23 when =26,s = 6,and n = 20,what is the value of the t-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 standard deviation is 3.74 years.Calculate the p-value for the test statistic used to test the claim that the mean years for all car owners is less than 7.5 years.

Last year,during an investigation of the time spent reading e-mails 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.

One survey conducted by a major leasing company determined that the Lexus is the favorite luxury car for 25% of leases in Atlanta.Suppose a US car manufacturer conducts its own survey in an effort to determine if this figure is correct.Of the 384 leases in Atlanta surveyed,79 lease a Lexus.Calculate the p-value associated with the test statistic.

Standard x-ray machines should give radiation dosages below 5.00 mill roentgens.To test a certain x-ray machine a sample of 36 observations is taken with a mean of 4.13 m.and a standard deviation of 1.91 m.Calculate the appropriate test statistic to test the hypotheses.