Besides their known long-term effects, do cigarettes also cause short-term illnesses such as colds? To help answer this question, a sample of smokers was drawn. Each person was asked to report the average number of cigarettes smoked per day and the number of days absent from work due to colds last year. What do the coefficients tell you about the relationship between smoking cigarettes and sick days because of colds?

Attempting to analyze the relationship between advertising and sales, the owner of a furniture store recorded the monthly advertising budget ($thousands) and the sales ($ millions) for a sample of 12 months. The data are listed here.

Advertising	23	46	60	54	28	33
Sales	$9.6$	$11.3$	$12.8$	$9.8$	$8.9$	$12.5$

Advertising	25	31	36	88	90	99
Sales	$12.0$	$11.4$	$12.6$	$13.7$	$14.4$	$15.9$

Calculate the least squares line and interpret the coefficients.

In the discussed problem, you used the summated rating to predict the cost of a restaurant meal (stored in Restaurants ). Determine the standard error of the estimate.

In the discussed problem, the percentage of alcohol was used to predict wine quality (stored in Vinho Verde ). For those data, SSR =21.8677 and SST=64.0000. Determine the standard error of the estimate.

What do you understand by the term standard error of estimate?

A manager of a local retail store analyzes the relationship between advertising and sales by reviewing the store's data for the previous six months.

$$\begin{array}{|c|c|} \hline \text { Advertising (in \$100s) } & \text { Sales (in \$1,000s) } \\ \hline 20 & 15 \\ \hline 25 & 18 \\ \hline 30 & 20 \\ \hline 22 & 16 \\ \hline 27 & 19 \\ \hline 26 & 20 \\ \hline \end{array}$$

a. Calculate the mean of advertising and the mean of sales.

b. Calculate the standard deviation of advertising and the standard deviation of sales.

c. Calculate and interpret the covariance between advertising and sales.

d. Calculate and interpret the correlation coefficient.

Refer to the exercise in this chapter where we were analyzing the relationship between advertising and sales. Compute the coefficient of determination and interpret this value.

Choose the best answer. A 10-question multiple-choice exam offers 5 choices for each question. Jason just guesses the answers, so he has probability 1/5 of getting any one answer correct. You want to perform a simulation to determine the number of correct answers that Jason gets. One correct way to use a table of random digits to do this is the following: (a) One digit from the random digit table simulates one answer, with 5 = right and all other digits = wrong. Ten digits from the table simulate 10 answers. (b) One digit from the random digit table simulates one answer, with 0 or 1 = right and all other digits = wrong. Ten digits from the table simulate 10 answers. (c) One digit from the random digit table simulates one answer, with odd = right and even = wrong. Ten digits from the table simulate 10 answers. (d) One digit from the random digit table simulates one answer, with 0 or 1 = right and all other digits = wrong, ignoring repeats. Ten digits from the table simulate 10 answers. (e) Two digits from the random digit table simulate one answer, with 00 to 20 = right and 21 to 99 = wrong. Ten pairs of digits from the table simulate 10 answers.

A standard deck of playing cards (with jokers removed) consists of 52 cards in four suits-clubs, diamonds, hearts, and spades. Each suit has 13 cards, with denominations ace, 2.3, +, 5, 6, 7, 8, 9, 10, jack, queen, and king. The jacks, queens, and kings are referred to as "face cards." Imagine that we shuffle the deck thoroughly and deal one card. The two-way table summarizes the sample space for this chance process based on whether or not the card is a face card and whether or not the card is a heart.

$$\text{Type of card}\\ \text{Suit} \begin{array}{l|c|c|c} & \text { Face card } & \begin{array}{c} \text { Nonface } \\ \text { card } \end{array} & \text { Total } \\ \hline \text { Heart } & 3 & 10 & 13 \\ \hline \text { Nonheart } & 9 & 30 & 39 \\ \hline \text { Total } & 12 & 40 & 52 \end{array}$$

Are the events "heart" and "face card" independent? Justify your answer.

An ordinary deck of playing cards has 52 cards. There are four suits-spades, hearts, diamonds, and clubs-with 13 cards in each suit. Spades and clubs are black; hearts and diamonds are red. If one of these cards is selected at random, what is the probability that it is a. a spade? b. red? c. not a club?

A normal pack of playing cards contains 52 cards. These are made up of four suits (hearts, diamonds, clubs and spades. Each suit consists of 13 cards. These are labelled Ace, 2, 3, 4, 5, 6, 7, 8, 9, 10, Jack, Queen and King. The hearts and diamonds are red; the clubs and spades are black. If a card is picked at random from a normal pack of cards, calculate the probability of picking: a) a heart, b) not a heart, c) a 4, d) a red King, e) a Jack, Queen or King, f) the Ace of spades, g) an even numbered card, h) a 7 or a club.

A standard deck of playing cards (with jokers removed) consists of 52 cards in four suits-clubs, diamonds, hearts, and spades. Each suit has 13 cards, with denominations ace, 2, 3, 4, 5, 6, 7, 8, 9, 10, jack, queen, and king. The jack, queen, and king are referred to as "face cards." Imagine that we shuffle the deck thoroughly and deal one card. Let's define events F: getting a face card and H: getting a heart. The two-way table summarizes the sample space for this chance process. $$ \text{Card} \\ \begin{array}{l|c|c|c} && \text { Face card } & \text { Nonface card } & \text { Total } \\ \hline &\text { Heart } & 3 & 10 & 13 \\ \text{Suit} & \hline \text { Nonheart } & 9 & 30 & 39 \\ \hline &\text { Total } & 12 & 40 & 52 \end{array} $$ Find $P\left(\mathrm{H}^{\mathrm{C}} \text { or } \mathrm{F}\right).$

A standard deck of playing cards (with jokers removed) consists of 52 cards in four suits- clubs, diamonds, hearts, and spades. Each suit has 13 cards, with denominations ace, 2, 3, 4, 5, 6, 7, 8, 9, 10, Jack, queen, and king. The jacks, queens, and kings are referred to as "face cards." Imagine that we shuffle the deck thoroughly and deal one card. Define events F: getting a face card and H: getting a heart. The two-way table summarizes the sample space for this chance process.

$$\begin{array}{ccc} & \text{Card} \\ \text{Suit} & {\begin{array}{l|c|c|c} & \text { Face card } & \text { Nonface card } & \text { Total } \\ \hline \text { Heart } & 3 & 10 & 13 \\ \hline \text { Nonheart } & 9 & 30 & 39 \\ \hline \text { Total } & 12 & 40 & 52 \end{array}} \\ \end{array}$$

Find $P\left(H^{C}\right.$ and $\left.F\right).$ Interpret this value in context.

In a standard deck of playing cards, there are four suits (red suits = hearts and diamonds, black suits = spades and clubs). Each suit has thirteen cards: Ace (A), 2, 3, 4, 5, 6, 7, 8, 9, 10, and the face cards Jack (J), Queen (Q), and King (K). In a single draw, what is the probability that you will draw a face card? A red card? A red face card?