The college admissions office at a local university usually admits 750 students and knows from previous experience that $25 \%$ of these students choose not to enroll at the university.

a. Construct the centerline and the upper and lower control limits for the $\bar{p}$ chart.

b. Assume that this year the university admits 750 students and 240 choose not to enroll at the university. Should the university be concerned? Explain.

The table shows the number of students who applied and the number of students attending selected universities. Graph the relation. $$ \begin{matrix} \text{University} & \text{Number Applied} & \text{Number Attending}\\ \text{Auburn University} & \text{13,264} & \text{4184}\\ \text{University of California-Davis } & \text{27,954} & \text{4412}\\ \text{University of Illinois-Urbana-Champaign} & \text{21,484} & \text{6366}\\ \text{University of Maryland-College Park} & \text{23,117} & \text{3912}\\ \text{State University of New York-Stony Brook} & \text{16,849} & \text{2415}\\ \text{The Ohio State University} & \text{19,563} & \text{5982}\\ \text{Texas A&M University} & \text{17,284} & \text{6949}\\ \end{matrix} $$

Glioblastoma is the most common and most deadly of brain tumors, and it kills most patients in a little over a year. The probability of survival for patients with a glioblastoma t years after diagnosis is approximated by the function $P(t)=\frac{100}{(1+0.14 t)^{9.2}} \ (0 \leq t \leq 10)$ where P is the percent of surviving patients. a. Compute $P(1)$ and $P(2),$ and interpret your results. b. Compute $P^{\prime}(1)$ and $P^{\prime}(2),$ and interpret your results.

Refer to the accompanying data file on happiness and age to answer the following questions.

a. Estimate a simple linear regression model with Happiness as the response variable and Age as the explanatory variable.

b. Use the sample regression equation to predict Happiness when Age equals 25, 50, and 75.

c. Construct a scatterplot of Happiness against Age. Discuss why your predictions might not be accurate.

For a sample of 41 New England cities, a sociologist studies the crime rate in each city (crimes per 100,000 residents) as a function of its poverty rate (in %) and its median income (in $\$ 1,000$ s). A portion of the regression results is shown in the following table.

$$\begin{array}{|l|r|c|c|c|c|} \hline \text { ANOVA } & \text { df } & \text { SS } & \text { MS } & F & \text { Significance F } \\ \hline \text { Regression } & 2 & 3549788 & 1774894 & 16.12513 & 8.5 \mathrm{E}-06 \\ \hline \text { Residual } & 38 & 4182663 & 110070.1 & & \\ \hline \text { Total } & 40 & 7732451 & & & \\ \hline \end{array}$$

a. Calculate the standard error of the estimate.

b. What proportion of the sample variation in crime rate is explained by the variability in the explanatory variables? What proportion is unexplained?

For a sample of 41 New England cities, a sociologist studies the crime rate in each city (crimes per 100,000 residents) as a function of its poverty rate (in %) and its median income (in $\$ 1,000$ s). He finds that $S S E=4,182,663$ and $S S T=7,732,451$.

a. Calculate the standard error of the estimate.

b. What proportion of the sample variation in crime rate is explained by the variability in the explanatory variables? What proportion is unexplained?

Osteoporosis is a disease that primarily affects postmeno- pausal women, causing decreased bone density and brittle bones that are vulnerable to fracture. The hormone calci- tonin is sometimes used to treat osteoporosis. Why?

Osteoporosis is a degenerative disease that primarily affects women over the age of 60 . A research analyst wants to forecast sales of StrongBones, a prescription drug for treating this debilitating disease. She uses the model Sales $=\beta_0+\beta_1$ Population $+\beta_2 \ln c o m e+\varepsilon$, where Sales refers to the sales of StrongBones (in $\$ 1,000,000$ s), Population is the number of women over the age of 60 (in millions), and Income is the average income of women over the age of 60 (in $\$ 1,000$ s). She collects data on 38 cities across the United States and obtains the following regression results:

$$\begin{array}{|l|c|c|c|c|} \hline & \text { Coefficients } & \text { Standard Error } & \text { t Stat } & \text { p-value } \\ \hline \text { Intercept } & 10.35 & 4.02 & 2.57 & 0.0199 \\ \hline \text { Population } & 8.47 & 2.71 & 3.12 & 0.0062 \\ \hline \text { Income } & 7.62 & 6.63 & 1.15 & 0.2661 \\ \hline \end{array}$$

interpret the slope coefficients.

A manufacturing process produces steel rods in batches of 1,000. The firm believes that the percent of defective items generated by this process is 5%.

a. Construct the centerline and the upper and lower control limits for the $\bar{p}$ chart.

b. An engineer inspects the next batch of 1,000 steel rods and finds that 6.2% are defective. Is the manufacturing process under control? Explain.

Un a multiple regression with four explanatory variables and 100 observations, it is found that $S S R=4.75$ and $S S T=7.62$.

a. Calculate the standard error of the estimate $s_e$.

b. Calculate the coefficient of determination $\mathrm{R}^2$.

c. Calculate adjusted $\mathrm{R}^2$.

Given that x is a hypergeometric random variable, compute p(x) for each of the following cases:

$$N = 6 , n = 2 , r = 2 , x = 2$$

Compare descriptive statistics and inferential statistics in research?

Descriptive statistics _____, while inferential statistics _____. a. indicate the significance of the data; summarize the data. b. describe data from experiments; describe data from surveys and case studies. c. are measures of central tendency; are measures of variance. d. determine if data can be generalized to other populations; summarize data. e. summarize data; assess if data can be generalized.

Determine whether the variable is qualitative or quantitative Explain your reasoning. Is the variable qualitative or quantitative?

• The variable is quantitative because age is found by measuring or counting.
• The variable is qualitative because age describes an attribute or characteristic
• The variable is quantitative because age describes an attribute or characteristic
• The variable is qualitative because age is found by measuring or counting.