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# Question 21 Suppose a health insurance company is interested in carrying out an investigation as to...

Question 21

Suppose a health insurance company is interested in carrying out an investigation as to the annual expenditures per household on their healthcare costs. In order to most accurately report their figures, the company decides to ensure “virtual certainty” about their estimates by using a Z value of 3.0 for their calculations. The company conducts a SRS of 843 households and determines the sample average household expenditures on healthcare is \$43,257.00.

A) Assume the company uses a σ=\$879.00. Calculate a confidence interval with virtual certainty for the average annual household expenditures on healthcare.

B) Interpret the interval calculated in the above response.

 A) (51154.22, 51223.82) B) We are virtually certain that the true population average household expenditures on healthcare lies within the interval A) (49254.77, 50154.26) B) We are somewhat certain that the true population average household expenditures on healthcare lies within the interval A) (43166.18, 43347.82) B) We are virtually certain that the true population average household expenditures on healthcare lies within the interval

Question 22

Suppose a mechanical engineering company is interested in patenting a new device that is intended to serve as the next generation of breast cancer screening beyond mammography. A key measurement statistic for the new device is its false positive rate. Suppose the current false positive rate for mammography is 12% with a σ of 3%, and the company tests the device on a SRS of 245 patients that results in an average false positive rate of 6.5%.

A) Can we assume that the new device improves upon the false positive rate for mammography? (Use α=0.05)

B) State and interpret your results.

 A) Ho: µ=.12, Ha: µ>0.12, Z statistic=250.13 pvalue of <0.001 B) There is sufficient evidence to reject the null hypothesis that the average false positive result for the new screening method is equal to 0.12. The new screening tool has a much higher false positive rate based on the results from the sample. A) Ho: µ=.12, Ha: µ<0.12, Z statistic=175.87 pvalue of <0.0001 B) There is not sufficient evidence to reject the null hypothesis that the average false positive result for the new screening method is equal to 0.12. The new screening tool has a much lower false positive rate based on the results from the sample. A) Ho: µ=.12, Ha: µ<0.12, Z statistic=276.53 pvalue of <0.0001 B) There is sufficient evidence to reject the null hypothesis that the average false positive result for the new screening method is equal to 0.12. The new screening tool has a much lower false positive rate based on the results from the sample.

Question 23

A researcher is interested in the effectiveness of a new program at reducing the average systolic blood pressure in a population with a new anti-hypertensive medication. The researcher wants to test the hypothesis that the mean difference in systolic blood pressure is greater than 40 mmHG. Which of the following represents the correct null and alternative hypotheses for the study?

 Ho: µ1 - µ2 = 0, Ha: µ1 - µ2 = 40 Ho: µ1 - µ2 = 40 Ha: µ1 - µ2 ≠ 40 Ho: µD = 40 Ha: µD >40 Ho: µD = 40 Ha: µD ≠40

Question 24

Suppose body mass index (BMI) varies approximately to the normal distribution in a population of boys aged 2-20. A national survey analyzed the BMI for American adolescents in this age range and found the µ=17.8 and the σ=1.9.

A) What is the 25th percentile of this distribution?

B) What is the z-score corresponding to finding a boy with at least a BMI 19.27?

C) What is the probability of finding a boy with at least this BMI?

 A) 20.11 B) 0.457 C) 0.1278 A) 16.52 B) 0.774 C) 0.2196 A) 17.87 B) 0.674 C) 0.4521

Question 25

Variability in a distribution that would be otherwise non-normal may tend towards normality with random sampling.

True

False

Question 26

Suppose X ~ N(275, 16)

A) Find the P(X≥294)

B) Find the P(255≤X≤297)

C) Find the 17th percentile of X

 A) 0.2251 B) 0.75 C) 274.31 A) 0.8745 B) 0.51 C) 224.46 A) 0.1175 B) 0.81 C) 259.73 Pg 162

Question 27

Suppose MCAT scores vary according to a normal distribution with µ=113 and σ=12.

A) Calculate the standard error of the mean when a simple random sample of 12 participants is collected.

B) Calculate the standard error of the mean when a simple random sample of 27 participants is collected.

C) Calculate the standard error of the mean when a simple random sample of 114 participants is collected.

 A) 2.61 B) 3.22 C) 1.97 A) 3.46 B) 2.31 C) 1.12 A) 2.98 B) 2.12 C) 0.99

Question 28

In a population of HIV positive subjects enrolled in a new trial to increase the prognosis and overall CD4 count, the CD4 levels vary approximately according to a normal distribution. The mean CD4 level is 394.7 cells/m3 and the standard deviation is 21.7 cells/m3. Of a sample of 48 participants, what is the probability of finding at least a CD4 count of 350?

 0.98 1.231 0.881

Question 29

Using a table for reference, determine the t value of t10, 0.05

 1.3721 1.8124 2.228

Question 30

A researcher is interested in investigating the power of his statistical test analyzing the success rate of increasing forced vital capacity (FVC) in children with asthma. Suppose the researcher conducted a z test for significance with a SRS of 74 on a population with a mean FVC of 84% with a null hypothesis that mean FVC was equal to 76%. The prior research determined the standard deviation was 1.2%. What was the power of the test at 95% confidence?

 ~99% ~95% ~90%

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