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Exam 8: Hypothesis Testing

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Question 81

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Standard x-ray machines should give radiation dosages below 5.00 mill roentgens (mil-r) . To test a certain x-ray machine, a sample of 36 observations is taken with a mean of 4.13 mil-r and a standard deviation of 1.91 mil-r. -Give a range for the p-value for this test.

A) 0.01 < p-value < 0.025
B) 0.001 < p-value < 0.005
C) 0.005 < p-value < 0.01
D) 0.05 < p-value < 0.10
E) 0.025 < p-value < 0.05

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Question 82

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What is the F-statistic for testing H₀: σ₁² ≤σ₂²,H_A: σ₂² > σ₁² at σ = .05 where n₁ = 16,n₂ = 19,s₁² = .03,s₂² = .02.

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Question 83

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The test of means for two related populations match the observations (matched pairs)in order to reduce the ________________ attributable to the difference between individual observations and other factors.

A microwave manufacturing company has just switched to a new automated production system.Unfortunately,the new machinery has been frequently failing and requiring repairs and service.The company has been able to provide its customers with a completion time of 6 days or less.To analyze whether the completion time has increased,the production manager took a sample of 36 jobs and found that the sample mean completion time was 6.5 days with a sample standard deviation of 1.5 days.At the 10% level of significance,test whether the completion time has increased.Assume time is normally distributed.

The manufacturer of an over-the-counter heartburn relief mediation claims that it product brings relief in less than 3.5 minutes, on average. To be able to make this claim the manufacturer was required 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 standard deviation was 1.1 minutes. Assume that time is normally distributed. -Give a range for the p-value for this test.

A paired difference experiment is an experiment in which there is relationship between the measurements in the different samples.

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 = 14.2 minutes. Assume times are normally distributed. -How much evidence do we have that the workers' claim is true?

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. Assume the number of days is approximately normally distributed. -The appropriate test statistic to test the hypotheses is _____.

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. Assume the number of days is approximately normally distributed. -How much evidence do we have that there is a slowdown?

Test H₀: σ₁² ≤σ₂²,H_A: σ₁² > σ₂² at alpha = .05 where n₁ = 16,n₂ = 19,s₁² = .03,s₂² = .02.

Test the equality of means at $\alpha$ = .05,where sample 1 has data:16,14,19,18,19,20,15,18,17,18,and sample 2 has data:13,19,14,17,21,14,15,10,13,15.Assume equal population variances,normally distributed populations,and independent random samples.

A manufacturer of a chemical used in glue, attempting to control the amount of a hazardous chemical its workers are exposed to, has given instructions to halt production if the mean amount in the air exceeds 3.0ppm. A random sample of 50 air specimens produced the following statistics: sample mean = 3.1 ppm, sample standard deviation = 0.5 ppm. Assume measurements are normally distributed. -How much evidence is there that the mean is greater than 3 ppm?

It is estimated that the average adult spends $123 in entertainment costs per month. Some believe this figure is too high and conducted a survey of 40 randomly selected adults. They found a mean of $113.03 per month was spent and a standard deviation of $25.99. -How much evidence do we have that the monthly entertainment costs are less than the estimate?

When testing a hypothesis about the mean of a population of paired differences in which two different observations are taken on the same units,the correct test statistic to use is based on the ____ distribution.

Given the following information about a hypothesis test of the difference between two variances based on independent random samples,what is the critical value of the test statistic at a significance level of .05? Assume that the samples are obtained from normally distributed populations. H_A: ?²_A > ?²_B, $\bar { X }$ ₁ = 12, $\bar { X }$ ₂ = 9,s₁ = 5,s₂ = 3,n₁ = 13,n₂ = 10.

It is estimated that the average adult spends $123 in entertainment costs per month. Some believe this figure is too high and conducted a survey of 40 randomly selected adults. They found a mean of $113.03 per month was spent and a standard deviation of $25.99. -Give a range for the p-value for this test.

A manufacturing operation consists of a unique system that produces an average of 15.5 jet engine propulsion parts every hour. After undergoing a complete overhaul, the system was monitored by observing the number of parts produced in each of 17 randomly selected one-hour periods. The mean is 15.42 with a standard deviation of 0.16. Assume the number of parts produced is approximately normal. -How much evidence do we have that the system differs from 15.5?

If the z statistic is incorrectly used in lieu of the t statistic when comparing two population means based on independent,small random samples from two normally distributed populations with unknown variances,then the probability of committing a Type II error __________.

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

A fast food company uses two management-training methods.Method 1 is a traditional method of training and Method 2 is a new and innovative method.The company has just hired 36 new management trainees.15 of the trainees are randomly selected and assigned to the first method,and the remaining 16 trainees are assigned to the second training method.After three months of training,the management trainees took a standardized test.The test was designed to evaluate their performance and learning from training.The sample mean score and sample standard deviation of the two methods are given below.The management wants to determine if the company should implement the new training method.Assume equal population variances and normally distributed populations. $\begin{array} { l c c } & \text { Mean } & \text { Standard deviation } \\\text { Method 1 } & 69 & 3.4 \\\text { Method 2 } & 72 & 3.8\end{array}$ -Is there sufficient evidence to conclude that the new training method is more effective than the traditional training method? What is the decision at alpha = .05?