At a major credit card bank, the percentages of people who historically apply for the Silver, Gold, and Platinum cards are $60 \%, 30 \%$, and $10 \%$, respectively. In a recent sample of customers responding to a promotion, of 200 customers, 110 applied for Silver, 55 for Gold, and 35 for Platinum. Is there proof to indicate that the percentages for this promotion may be different from the historical proportions?

e) Using the critical value, what do you conclude about the null hypothesis at $\alpha=0.05$?

At a major credit card bank, the percentages of people who historically apply for the Silver, Gold, and Platinum cards are $60 \%, 30 \%$, and $10 \%$, respectively. In a recent sample of customers responding to a promotion, of 200 customers, 110 applied for Silver, 55 for Gold, and 35 for Platinum. Is there proof to indicate that the percentages for this promotion may be different from the historical proportions?

d) Find the $\alpha=0.05$ critical value for the $\chi^2$ distribution with the appropriate number of $\mathrm{df}$.

At a major credit card bank, the percentages of people who historically apply for the Silver, Gold, and Platinum cards are $60 \%, 30 \%$, and $10 \%$, respectively. In a recent sample of customers responding to a promotion, of 200 customers, 110 applied for Silver, 55 for Gold, and 35 for Platinum. Is there proof to indicate that the percentages for this promotion may be different from the historical proportions?

c) What does that say about the null hypothesis?

Look again at the earlier exercise's regression output for the calorie and sodium content of hot dogs.

What's the value of the standard error of the slope of the regression line?

Look again at the earlier exercise's regression output for age and cholesterol level. (Data in Framingham)

What's the value of the standard error of the slope of the regression line?

The earlier exercise displays computer output examining the association between the length of a movie and its cost.

a) Check the assumptions and conditions for inference.

What other assumptions or conditions are required for using inference for regression on these data? Check that these conditions are satisfied and then describe your findings.

Davos Company performed services on account for $160,000 in 2016. Davos collected$120,000 cash from accounts receivable during 2016, and the remaining $40,000 was collected in cash during 2017.

Required

Record the 2016 transactions in T-accounts.

What can the hockey coach in the earlier exercise conclude about shooting and scoring goals from the fact that the P-value < 0.0001 for the slope of the regression line? Write a sentence in context.

A prestigious college is interested in factors that might be associated wit h better graduation rates . The administrators wonder whether there is a relationship between acceptance rates and graduation rates . Using the regression output, identify the standard deviation of the residuals and explain what it means in the context of the problem. $\newline$ Dependent variable is 6-Year Graduation Rate $\newline$ R-squared= 69.6% $\newline$ s = 2.86 with 50 - 2 = 48 degrees of freedom $\newline$

$$\begin{alignat*}{7} \textbf{Variable} \quad &\textbf{Coefficient} \quad &\textbf{SE(Coeff)} \quad &\textbf{t-Rate} \quad &\textbf{P-Value} \\ \text{Intercept} \quad & 97.663 \quad & 0.84406 \quad & 114.999 \quad & <0.0001\\ \text{Acceptance Rate} \quad & -0.25101 \quad & 0.023951 \quad & -10.480 \quad & <0.0001 \end{alignat*}$$

A college hockey coach collected data from the 2016-2017 National Hockey League season. He hopes to convince his players that the number of shots taken has an effect on the number of goals scored. The coach performed a preliminary analysis, using the scoring statistics from 65 offensive players who had played at least 44 games by the middle of the season. (If you use the data file, note that it includes defensive players as well. Use the variable Offense to select the players in this analysis.) He predicts Goals from a number of Shots. a) Discuss each of the conditions and assumptions required for him to proceed with the regression analysis. b) Write the regression model and explain what the slope coefficient means in this context.

The response variable is Goals

R-squared $=49.9 \%$

$s=2.983$ with $65-2=63$ degrees of freedom

$$\begin{array}{lcccr}\text { Variable } & \text { Coefficient } & \text { SE(Coeff) } & \text { t-ratio } & \text { P-value } \\ \text { Intercept } & 1.13495 & 1.231 & 0.922 & 0.3602 \\ \text { Shots } & 0.099267 & 0.0125 & 7.93 & <0.0001\end{array}$$

At a major credit card bank, the percentages of people who historically apply for the Silver, Gold, and Platinum cards are 60%, 30%, and 10%, respectively. In a recent sample of customers responding to a promotion of 200 customers, 110 applied for Silver, 55 for Gold, and 35 for Platinum. Is there evidence to suggest that the percentage s for this promotion may be different from the historical proportions? a) What is the expected number of customers applying for each type of card in this sample if the historical proportions are still true? b) Compute the

$$X^2$$

statistic. c) How many degrees of freedom does the

$$X^2$$

statistic have?

Does the statistic you calculated in the earlier exercise seem large in comparison to this mean? Describe briefly.

At a major credit card bank, the percentages of people who historically apply for the Silver, Gold, and Platinum cards are $60 \%, 30 \%$, and $10 \%$, respectively. In a recent sample of customers responding to a promotion, of 200 customers, 110 applied for Silver, 55 for Gold, and 35 for Platinum. Is there proof to indicate that the percentages for this promotion may be different from the historical proportions?

a) If the customers apply for the three cards according to the historical proportions, about how big, on average, would you expect the $\chi^2$ statistic to be (what is the mean of the $\chi^2$ distribution)?