Question 1 (a)

  • Summarizing Distributions

    • Center: Median / Mean

    • Shape: Skew left / right

    • Spread: SD / IQR

    • Outlier

Question 1 (b)

Corporation A Corporation B $30 $40 $50 $60 $70 $80 Yearly Salary (thousands)

(i) Five years after starting, at least 3 out of 30 (10%) of the salaries at Corporation A are greater than the maximum salary at Corporation B. If I accept the offer from Corporation A, I might be able to at Corporation A than at Corporation B. (ii) Five years after starting, the minimum salary at Corporation B is greater than at Corporation A. In fact, at Corporation A it looks like some people are still making the starting salary of $36,000 and never received a raise in the five years since they were hired. So if I work at Corporation A, I might never receive a raise in salary.

Question 4

Step 1: States a correct pair of hypotheses. Let pasp represent the population proportion of adults similar to those in the study who would have developed colon cancer within the six years of the study if they had taken a low-dose aspirin each day. Similarly, let pplac represent the population proportion of adults similar to those in the study who would have developed colon cancer within the six years of the study if they had taken a placebo each day. The hypotheses to be tested are Ho : pasp pplac versus Ha : pasp < pplac or equivalently, Ho : pasp O versus H : p a asp — Pplac < O. — Pplac Step 2: Identifies a correct test procedure (by name or by formula) and checks appropriate conditions. The appropriate procedure is a two-sample z-test for comparing proportions. Because this is a randomized experiment, the first condition is that the volunteers were randomly assigned to one treatment group or the other. The condition is satisfied because we are told that the volunteers were randomly assigned to take a low-dose aspirin or a placebo. The second condition is that the sample sizes are large, relative to the proportions involved. The condition is satisfied because all sample counts are large enough; that is, 15 with colon cancer in aspirin group, 26 with colon cancer in placebo group, 500 — 15 = 485 cancer-free in aspirin group, and 500 — 26 = 474 cancer-free in placebo group.

Step 3: Calculates the appropriate test statistic and p-value. — = 0.030 and The sample proportions who developed colon cancer are p asp — 500 15 + 26 The combined sample proportion who developed colon cancer is pcombined — 26 = 0.052. - 500 = 0.041. The test statistic is z — stribution. 0.030 - 0.052 0.041(1 - 0.041) A + 500 500 + 500 —1.75 (—1.7542 from calculator). 1 500 The p-value is P(Z —1.75) = 0.0401 (0.0397 from calculator), where Z has a standard no

Step 4: States a correct conclusion in the context of the study, using the result of the statistical test. Because the p-value is less than the given significance level of a = 0.05, we reject the null hypothesis. The data provide convincing statistical evidence that the proportion of all adults similar to the volunteers who would develop colon cancer if they had taken a low-dose aspirin every day is less than the proportion of all adults similar to the volunteers who would develop colon cancer if they had not taken a low-dose aspirin every day.

Question 5 (a)

  • Response should be given in context

    There is a moderately strong, positive, linear relationship between height and arm span so that taller students tend to have lonqer arm spans.

Question 6 (b)

UNIMODAL BIMODAL log (molar weight) \[g/mole\]

Question 6 (c)

Method 2 would result in less variability in the sample of 200 tortillas on a given day because the sample comes from only one production line. Because the distributions of diameters are not the same for the two production lines, selecting tortillas from both lines as in Method 1 would result in more variable sample data.

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