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Marital Status. The probability that a randomly chosen 40-year-old woman is divorced is about 0.15. this probability is a long-run proportion based on all the millions of women aged 40. Let's suppose that the proportion stays at 0.15 for the next 20 years. Bridget is now 20 years old and is not married.
(a) Bridget thinks her own chances of being divorced at age 40 are about 5%. Explain why this is a personal probability.
(b) Give some good reasons why Bridget's personal probability might differ from the proportion of all women aged 40 who are divorced
(c) You are a government official charged with looking into the impact of the Social Security system on middle-aged divorced women. You care only about the probability 0.15, not about anyone's personal probability. Why?
Can we conclude that there is a positive association between the size of the home and the selling price? Use the .05 significance level.
Provide a 99% confidence interval for the population proportion of college students who worked to pay for tuition and living expenses.
Suppose that 1% of all the students seeking treatment at the school infirmary have mono. Of the students who do have mono, 90% complain of a sore throat. Of the students who do not have mono, 30% also have sore throats.
EBook is a digital book provider that sells their downloaded product through both Anason and Bairnes-Nolb. Anason requires that EBook use a different format than they use for Bairnes-Nolb.
Here is a scatterplot of average crawling age versus average outdoor temperature six months after birth followed by a plot of the residuals versus average outdoor temperature six months after birth.
The sales manager had predicted, before the business started, that year 1's sales would be 410 air conditioners. Using exponential smoothing with a weight of alpha = 0.30, develop forecasts for years 2 through 6.
Describe when a z-test should be performed as opposed to a t-test? Which (if any) can we use all the time? Why or why not?
For each of the F statistics given above find the degrees of freedom and an approximate P-value. Summarize the results of these tests.
A major problem resulting from the lack of randomization in a cohort study is: the possibility that a factor that led to the exposure, rather than the exposure itself, might have caused the disease.
Is the gender distribution for theater goers significantly different from the distribution for the general college? Test at the .05 level of significance.
ANOVA is a powerful statistical test. How does ANOVA differ from other parametric tests? What are the conditions that must be met to use a one-way ANOVA?
Suppose we have observations x1, x2, . . . , xn. Prove that the sum of deviations of the observations from their arithmetic mean is always equal to zero.
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