Question 1

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 1 0.1 milligram per cubic centimetre (mg/cc). A random sample of four containers gave potency readings equal to 4.94, 5.10, 5.02, and 4.91 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 Ho: M = 5 versus Ha: M > 5 O Ho: M = 5 versus H: H # 5 OH: u = 5 versus Ha: 1 = 5 O Ho: M = 5 versus HA: M 5 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 not rejected. There is insufficient evidence to indicate that the mean potency differs from 5 mg/cc. O Ho is not rejected. There is sufficient evidence to indicate that the mean potency differs from 5 mg/cc. O Ho is rejected. There is sufficient evidence to indicate that the mean potency differs from 5 mg/cc. O Ho is rejected. There is insufficient evidence to indicate that the mean potency differs from 5 mg/cc. (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 determ 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- 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 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 dec places.) 1-2. Null and alternative hypotheses: OH: 02 > 0.0011 versus H: 0 0.2 O Ho: 02 = 0.2 versus H: 02 # 0.2 OH: 02 = 0.0011 versus H: 0 0.0011 3. Test statistic: xThe K2 test statistic can be computed as follows where DJ. is the observed count and Er. is the expected count for each of the r = 1, 2 categories. 2 _ [0. E32 X r r ZE,. We will find each 0: observed count in the data and we can calculate the E, expected counts using the hypothesized probabilities p1 = 0.75 and p2 = 0.25 with the formula E, = npr where n is the total number of observations that have been categorized. Since the geneticist germinated 100 seeds, n = \\:| . Flnd the E1 expected counts for the red petal category with probabilityr p]. E1 = npl (EMU-m = |:| Find the E2 expected counts for the Streaky petal category with probability p2. E = 111p2 0:00:25) = E A national home builder wants to compare the prices per 2.4 cubic metres board of standard or better grade Douglas fir framing lumber. He randomly selects five suppliers in each of the four provinces where the builder is planning to begin construction. The prices are given in the table. Province 1 ($) 2 ($) 3 ($) 4 ($) 243 216 232 245 235 220 225 250 238 205 235 238 247 213 228 255 252 220 240 257 (a) What type of experimental design has been used? O nonrandomized design O completely randomized design with five independent samples O completely randomized design with four independent samples O randomized block design with five blocks O randomized block design with four blocks (b) Construct the analysis of variance table for this data. (Round your answers to one decimal place.) Source df SS MS Treatments Error Total(c) Do the data provide sufficient evidence to indicate that the average price per 2.4 cubic metres of Douglas fir differs among the four provinces? Test using a = 0.05. (Round your answers to two decimal places.) 1-2. Null and alternative hypotheses: Hoi My = M2 = My = #4 Versus He: One or more pairs of population means differ O Hoit, = H2 = 43 = HA versus He: None of the population means are the same O Hoi Hy 5. Conclusion: O H is not rejected. There is sufficient evidence to indicate a difference in the average prices for the four provinces. O H is not rejected. There is insufficient evidence to indicate a difference in the average prices for the four provinces. O Ho is rejected. There is insufficient evidence to indicate a difference in the average prices for the four provinces. O Ho is rejected. There is sufficient evidence to indicate a difference in the average prices for the four provinces