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To properly treat patients, drugs prescribed by physicians must have a potency that is accurately defined. Consequently, not only must the distribution of potency values for shipments of a drug have a mean value as specified on the drug's container, but also the variation in potency must be small. Otherwise, pharmacists would be distributing drug prescriptions that could be harmfully potent or have a low potency and be ineffective. A drug manufacturer claims that its drug is marketed with a potency of 5 + 0.1 milligram per cubic centimetre (mg/cc). A random sample of four containers gave potency readings equal to 4.95, 5.08, 5.02, and 4.89 mg/cc. (a) Do the data present sufficient evidence to indicate that the mean potency differs from 5 mg/cc? (Use a = 0.05. Round your answers to three decimal places.) 1-2. Null and alternative hypotheses: O H: M = 5 versus Ha: M $ 5 O Ho: M 5 O Ho: M = 5 versus Ha: H > 5 O Ho: M # 5 versus Ha: M = 5 O Ho: M = 5 versus Ha: M t 0.0011 versus Ha: 62 0.2 O Ho: 02 = 0.0011 versus Ha: 62 0.0011(b) Do the data present sufficient evidence to indicate that the variation in potency differs from the error limits specified by the manufacturer? (HINT: It is sometimes difficult to determine exactly what is meant by limits on potency as specified by a manufacturer. Since it implies that the potency values will fall into the interval 5.0 + 0.1 mg/cc with very high probability-the implication is always-let us assume that the range 0.2; or (4.9 to 5.1), represents 60, as suggested by the Empirical Rule. Note that letting the range equal 60 rather than 40 places a stringent interpretation on the manufacturer's claim. We want the potency to fall into the interval 5.0 + 0.1 with very high probability.) (Use a = 0.05. Round your answers to three decimal places.) 1-2. Null and alternative hypotheses: O Ho: 62 = 0.2 versus Ha: 02 # 0.2 O Ho: 02 > 0.0011 versus Ha: 62 0.2 O Ho: 02 = 0.0011 versus Ha: 62 0.0011 3. Test statistic: x2 4. Rejection region: If the test is one-tailed, enter NONE for the unused region. x - > x 2 5. Conclusion: O Ho is not rejected. There is insufficient evidence to indicate that the variation in potency differs from the specified error limits. O Ho is rejected. There is sufficient evidence to indicate that the variation in potency differs from the specified error limits. O Ho is not rejected. There is sufficient evidence to indicate that the variation in potency differs from the specified error limits. O Ho is rejected. There is insufficient evidence to indicate that the variation in potency differs from the specified error limits. leed Help? Read ItA random sample of size n = 7 from a normal population produced these measurements: 1.6, 3.5, 1.6, 2.1, 3.3, 3.0, 3.1. (a) Calculate the sample variance, s2. (Round your answer to five decimal places.) $2 = (b) Construct a 95% confidence interval for the population variance, of. (Round your answers to three decimal places.) to (c) Test Ho: oz = 0.8 versus Ha: 02 + 0.8 using a = 0.05. State your conclusions. State the test statistic. (Round your answer to four decimal places.) x2 = [ State the rejection region. (If the test is one-tailed, enter NONE for the unused region. Round your answers to four decimal places.) * 2 > State the conclusion. O Ho is rejected. There is insufficient evidence to indicate that the population variance is different from 0.8. O Ho is not rejected. There is sufficient evidence to indicate that the population variance is different from 0.8. O Ho is not rejected. There is insufficient evidence to indicate that the population variance is different from 0.8. O Ho is rejected. There is sufficient evidence to indicate that the population variance is different from 0.8. (d) What is the approximate p-value for the test in part (c)? O p-value 0.200 You may need to use the appropriate appendix table or technology to answer this question. Need Help? Read ItA psychology class performed an experiment to compare whether a recall score in which instructions to form images of 25 words were given is better than an initial recall score for which no imagery instructions were given. Twenty students participated in the experiment with the following results. With Without With Without Student Imagery Imagery Student Imagery Imagery 1 21 5 18 24 10 12 21 17 21 13 21 10 A W N 17 14 16 13 5 23 6 15 25 8 6 19 12 16 21 10 19 Co 17 25 22 1 00 V 18 10 18 21 14 17 19 20 12 10 20 20 24 13 Does it appear that the average recall score is higher when imagery is used? (Use a = 0.01 and /with imagery - "without imagery = "d.) State the null and alternative hypotheses. O Ho: My = 0 versus Ha: Md 0 O Ho: Mg = 0 versus Ha: Hd > 0 State the test statistic. (Round your answer to three decimal places.) t = State the rejection region. (If the test is one-tailed, enter NONE for the unused region. Round your answers to three decimal places.) t> t 0 O Ho: My = 0 versus Hai Had 0 O Ho: My = 0 versus Ha: Hd * 0 3. Test statistic: t = 4. Rejection region: If the test is one-tailed, enter NONE for the unused region. t> 5. Conclusion: O Ho is rejected. There is sufficient evidence to indicate a bias in the air-based temperature readings. O Ho is not rejected. There is sufficient evidence to indicate a bias in the air-based temperature readings. Ho is not rejected. There is insufficient evidence to indicate a bias in the air-based temperature readings. O Ho is rejected. There is insufficient evidence to indicate a bias in the air-based temperature readings. b) Estimate the difference in mean temperatures between ground- and air-based sensors using a 95% confidence interval. (Round your answers to three decimal places.) OC to OC (c) How many paired observations are required to estimate the difference between mean temperatures for ground- versus air-based sensors correct to within 0.3C, with probability approximately equal to 0.95? (Round your answer up to the nearest whole number.) observations Need Help? Read ItAn advertisement for a popular supermarket chain claims that it has had consistently lower prices than four other full-service supermarkets. As part of a survey conducted by an "independent market basket price-checking company," the average weekly total, based on the prices (in $) of approximately 95 items, is given for two different supermarket chains recorded during 4 consecutive weeks in a particular month. Week Advertiser ($) Competitor ($) 254.35 256.10 2 240.68 255.60 3 231.94 255.21 234.23 261.16 (a) Is there a significant difference in the average prices for these two different supermarket chains? (Use a = 0.05. Round your answers to three decimal places.) 1-2. Null and alternative hypotheses: O Ho: My = 0 versus Ha: H # 0 O Ho: My 0 O Ho: Mg = 0 versus Ha: Hd > 0 O Ho: Mg # 0 versus Ha: Hd = 0 O Ho: My = 0 versus Ha: Hd t 0.200 c) Construct a 99% confidence interval for the difference in the average prices for the two supermarket chains. (Round your answers to two decimal places. ) $ 1 to $A paired-difference experiment consists of n = 17 pairs, d = 5.5, and s = 256. Suppose you wish to detect / > 0. (a) Give the null and alternative hypotheses for the test. O Ho: Md # 0 versus Ha: Hd > 0 OH: Mg > 0 versus Ha: Ha 0 O Ho: Mg = 0 versus Ha: Hd > 0 OH: Mg > 0 versus Ha: Hd = 0 (b) Conduct the test and state your conclusions. (Use a = 0.05.) State the test statistic. (Round your answer to three decimal places.) t = State the rejection region. (If the test is one-tailed, enter NONE for the unused region. Round your answers to three decimal places.) t > . 0. O Ho is not rejected. There is insufficient evidence to indicate that MJ > 0. O Ho is not rejected. There is sufficient evidence to indicate that / > 0. O Ho is rejected. There is insufficient evidence to indicate that M > 0.A paired-difference experiment was conducted using n = 10 pairs of observations. (a) Test the null hypothesis Ho: (M1 - M2) = 0 against Ha: (M1 - M2) # 0 for a = 0.05, d = 0.3, and s 2 = 0.16. State the test statistic. (Round your answer to three decimal places.) t = Give the approximate p-value for the test. O p-value 0.200 State the conclusion. O Ho is rejected. There is sufficient evidence to indicate a difference in the two population means. O Ho is not rejected. There is insufficient evidence to indicate a difference in the two population means. O Ho is rejected. There is insufficient evidence to indicate a difference in the two population means. O Ho is not rejected. There is sufficient evidence to indicate a difference in the two population means. (b) Find a 95% confidence interval for (M1 - M2). (Round your answers to three decimal places.) to (c) How many pairs of observations do you need if you want to estimate (M, - M2) correct to within 0.1 with probability equal to 0.95? (Round your answer up to the nearest whole number.) pairs of observations
