Assume That the Standard Deviation of the Population,Sigma, Is Known

The principal of a middle school claims that the mean test score of the seventh-graders at his school is higher than 72.1. You wish to test this claim at the 0.05 level of significance. The mean score for a random sample of 100 seventh-graders is 75.7 with a standard deviation of 15.2. What criterion would be used for rejecting the null hypothesis, given the claim that µ 72.1?

Assume that the standard deviation of the population,sigma, is known.

Answer Reject Ho if test statistic > 1.645. Reject Ho if test statistic > 1.96 or < -1.96. Reject Ho if test statistic > 1.96. Reject Ho if test statistic < 1.645. 6 points

Question 2 A chicken farmer in Grayslake claims that his chickens have a mean weight of 58 ounces. The farmer takes a random sample of 36 chickens and finds a mean weight of 59.2 ounces and a standard deviation of 3 ounces. In a hypothesis test, what criterion would be used for rejecting the farmer's claim at the 10 percent level of significance?Assume that the standard deviation of the population, sigma, is known.

Answer Reject Ho that µ = 58 ounces if test statistic > 1.28 or < -1.28. Reject Ho that µ = 58 ounces if test statistic > 1.28. Reject Ho that µ = 58 ounces if test statistic > 1.645 or < -1.645. Reject Ho that µ = 58 ounces if test statistic > 1.645. 6 points

Question 3 What is the margin of error, given that 95% confidence interval; n = 12; = 55.7, and s = 6.7? Answer 5.108 3.831 4.257 3.193 6 points

Question 4 A laboratory tested 12 chicken eggs and found that the mean amount of cholesterol was 224 milligrams with s = 18.5 milligrams. What is the 95 percent confidence interval for the true mean cholesterol content of all such eggs? I. 214.4 < µ < 233.6 II. 217.7< µ < 230.3 III. 213.5 < µ < 234.5 IV. 212.2 < µ < 235.8

Answer Please refer to answer choice I above. Please refer to answer choice II above. Please refer to answer choice III above. Please refer to answer choice IV above. 6 points

Question 5 Find the value of the linear correlation coefficient r. The paired data below consist of the temperatures on randomly chosen days and the amount a certain kind of plant grew (in millimeters): Answer 0.256 -0.210 0 0.196 6 points I need the data here

Question 6 Use the margin of error, confidence level, and standard deviation s to find the minimum sample size required to estimate an unknown population mean µ: Margin of error: $130, confidence level: 99%, s = $501.

Answer 57 1 50 99 6 points

Question 7 Assume that X has a normal distribution. The mean is 137.0 and the standard deviation is 5.3. What is the probability that X is between 134.4 and 140.1? Answer 0.4069 0.8138 1.0311 0.6242 6 points

Question 8

If Z is a standard normal variable, what is the probability P (Z > 0.59)? Answer 0.7224 02224 02776 02190 6 points

Question 9 A drug company claims that over 70% of all physicians recommend their drug. 1200 physicians were asked if they recommend the drug to their patients. 45.00% said yes. Ho: p = 0.7. Confidence level: 95%. What is the value of the appropriate test statistic used to test the null hypothesis? Answer -17.01-24.57 -37.80 -18.90 6 points

Question 10 Identify the null hypothesis Ho and the alternative hypothesis H1. A researcher claims that the amounts of acetaminophen in a certain brand of cold tablets have a standard deviation different from the = 3.3 mg claimed by the manufacturer. Ho: s ? l 3.3 mg, H1: s = 3.3 mg II. Ho: s = 3.3 mg, H1: s ?3.3 mg III. Ho: s = 3.3 mg, H1: s ? 3.3 mg IV. Ho: s = 3.3 mg, H1: s > 3.3 mg Answer Please refer to answer choice I above. Please refer to answer choice II above Please refer to answer choice III above Please refer to answer choice IV above 6 points

Answer: H0: s=3.3 H1: s≠3.3

Question 11 The principal of a middle school claims that test scores of the seventh-graders at his school vary less than the test scores of the seventh-graders at a neighboring school, which have variation described by sigma = 14.7. Assuming that a hypothesis test of the claim has been conducted and that the conclusion is to reject the null hypothesis, state the conclusion in nontechnical terms Answer There is sufficient evidence to support the claim that the standard deviation is greater than 14.7. There is sufficient evidence to support the claim that the standard deviation is less than 14.7. There is not sufficient evidence to support the claim that the standard deviation is less than 14.7. There is not sufficient evidence to support the claim that the standard deviation is greater than 14.7. 6 points Question 12 What is the margin of error for the 95% confidence interval used to estimate the population proportion, given that n = 260 and x = 70? Answer 0.0539 0.0566 0.0485 0.0647 6 points Question 13 Use the given level of confidence and sample data to construct a confidence interval for the population proportion p: n = 143, x = 92; 90 percent. Answer 0.576 < p< 0.710 0.580 < 0.706 0.574 < 0.706 0.559 < p< 0.687 6 points Question 14 What is the value of the linear correlation coefficient r? Answer 0 -0.632 0.632 0.562 6 points Question 15 Scores on an English test are normally distributed with a mean of 35 and a standard deviation of 7.4. What is the score that separates the top 59% from the bottom 41%? Answer 30.6 36.7 39.4 33.3 6 points Question 16 Do one of the following, as appropriate: Find the critical value , find the critical value , or state that neither the normal nor the t distribution applies. 95% level of significance; n = 11; sigma s is known; population appears to be very skewed. I. = 1.96 II. = 2.228 III. Neither the normal nor the t distribution applies. IV. = 1.81 Answer Please refer to answer choice I above. Please refer to answer choice II above. Please refer to answer choice III above. Please refer to answer choice IV above. 6 points Question 17 Assume that the data has a normal distribution and the number of observations is greater than fifty. Also assume that the standard deviation of the population, s, is known. Find the critical value or values used to test a null hypothesis: a = 0.03; H1 is µ < 290. Answer 1.88 ±2.17 ±1.88 -1.88 6 points Question 18 Find the critical value or values for the given hypothesis, sample size, and significance level. Assume that the standard deviation of the population, s, is unknown. H1: µ > 3.74, n = 13, a = 0.01. Answer -2.650 2.650 2.681 -2.681 6 points Question 19 Use the confidence level and sample data to find the margin of error E: Systolic blood pressures for women aged 18-24: 94% confidence; n = 100, = 113.8 mm Hg, sigma s = 12.8 mm Hg. Answer 2.4 mm Hg 2.1 mm Hg 10.0 mm Hg 52.5 mm Hg 6 points Question 20 Use the confidence level and sample data to find the margin of error E: The duration of telephone calls directed by a local telephone company: sigma s = 3.7 minutes, n = 540, 92 percent confidence. Answer 0.012 minutes 0.006 minutes 0.279 minutes 0.091 minutes 6 points Question 21 A population is normally distributed with a standard deviation sigma = 349. We wish to test the hypotheses Ho: µ = 66,818; H1 = µ > 66,818. A 123-item sample has a mean = 66,399.2. What is the value of the test statistic? Answer -0.11 4233.38 -13.31 -1188.3 6 points Question 22 What is the minimum sample size you should use to assure that your estimate of will be within the required margin of error around the population p? Margin of error: 0.04; confidence level: 90%; from a prior study, is estimated by 0.20. Answer 240 271 11 813 6 points Question 23 What is the minimum sample size you should use to assure that your estimate of will be within the required margin of error around the population p? Margin of error: 0.007; confidence level: 99%; are unknown. Answer 184 33,830 135,319 541,276 6 points Question 24 270 randomly selected light bulbs were tested in a laboratory, 98 lasted more than 500 hours. Find a point estimate of the true proportion of all light bulbs that last more than 500 hours. Answer 0.359 0.266 0.363 0.637 6 points Question 25 The following confidence interval is obtained for a population proportion, p: 0.746 < p < 0.782. What is the margin of error, E? Answer 0.019 0.018 0.036 0.764