Question

1. [7 – 3] In terms of acting, Betty White is known for starring on 3 different long running television shows (The Mary Tyler Moore Show, The Golden Girls and Hot In Cleveland). Those three shows averaged 23.7 shows per season. However, it seems that shows are producing few episodes per season, and Betty decides to put that to the test. She takes a random sample of long running television programs and determined the number of episodes in their most recent season below:

13, 26, 23, 18, 24, 18, 19, 13, 13, 15, 16, 21, 20, 16, 26

You may assume that the data comes from a normal distribution.

1. Construct a 95% confidence interval for the average number of episodes per season for a television program

2. Based on your answer to (a), can we say that the average number of episodes per season is lower than the value 23.7, the average number of episodes for the shows that Betty starred in? Explain.

2. [5] Between 2006 and 2009, Betty appeared in 23 episodes of The Bold and The Beautiful. The work was quite different from her time on sitcoms. This led her to think about the following hypotheses:

H₀: Soap opera acting is the same difficulty as sitcom acting

H_a: Soap opera acting is harder than sitcom acting

Describe what a Type I error would look like in the context of this scenario.

3. [10] While playing the role of Catherine Piper on Boston Legal, Betty White “killed” the character of Bernard Ferrion (played by Leslie Jordan). Catherine ended being found not guilty, but it led Betty to wonder: are men and women treated differently when convicted of murder? As a result, Betty took two random samples of convicted murderers, given below, and determined how long the sentences were.

Men: 25, 30, 50, 25, 20, 30, 40, 25, 30, 25, 75, 25, 15

Women: 25, 15, 20, 15, 20, 25, 15, 30, 25, 40

You may assume the data comes from normal distributions. At the .05 level of significance, is there evidence to show that men get longer sentences for murder than women?

4. [10] Betty is a common diminutive of the name Elizabeth. As a result, many people think Betty White’s real first name is Elizabeth – but how large a proportion? Betty took a random sample of 265 people and found that 147 of them believe that Betty White’s real first name is Elizabeth. At the .05 level of significance, is there evidence that a majority (more than 50%) of all people think Betty White’s real first name is Elizabeth?

(Side note: Betty White’s real first name is… Betty – she says that it isn’t “short” for anything)

5. [10] In 1995, Betty White received a star on the Hollywood Walk of Fame – and her star is right near the star of her late husband, Allen Ludden. There are many couples that both have stars on the Hollywood Walk of Fame. This led Betty to wonder – is there a difference in the age between the husband and wife when they get their Hollywood star? As a result, Betty took a random sample of heterosexual couples that both have stars on the Hollywood Walk of Fame and recorded the age at which they received their star, given below.

Husband	62	67	51	62	73	47	55	60	80	76	42
Wife	55	68	56	54	60	50	49	58	75	74	49

At the .05 level of significance, is there evidence that there is a difference in the ages when husbands and wives get their Hollywood Walk of Fame star?

6. [10] For 19 years, Betty was hostess of the Tournament of Roses Parade (which is every year before the Rose Bowl). Of all the parades on television that exist, which is the favorite? A random sample of people was taken, with the results summarized below:

	Men	Women	Total
Rose Parade	42	55	97
Thanksgiving Parade	75	162	237
Parades? Who cares!	218	182	400
Total	335	399	734

At the .05 level of significance, is there an association between gender and favorite parade on television?

7. [7 – 3] Betty starred on a great number of game shows – and perhaps my favorite was Match Game. While Betty was a great player, did she do better with some contestants than others? Betty took a random sample of Match Game episodes and found that she matched the male contestants 264 out of 385 times and matched the female contestants 294 out of 377 times.

1. Construct a 95% confidence interval for the difference in the proportion of the time Betty would match male contestants and the proportion of the time Betty would match female contestants.

2. Based on your answer to (a), can we conclude that Betty matched one group of contestants better than the other?

8. [12] There is a Facebook group devoted to The Golden Girls. On a regular basis, the group poses the question: Which Golden Girl was your favorite? A recent random sample of members of the Facebook group answered the question, given in the table below.

GG Character	Rose	Sophia	Dorothy	Blanche	I can’t decide!
Frequency	42	73	38	64	53

At the .05 level of significance, is there evidence to show that the distribution of favorite Golden Girls character is not uniform? (meaning, not an equal distribution)

9. [3 – 5 – 3 – 2 – 2] In 2010, Betty White (at age 88!) hosted an episode of Saturday Night Live, becoming the oldest host the show has ever had. Most people know that she was the oldest. However, what about the second oldest? Do people have an idea how old the second oldest guest host was? A random sample of people was taken; these people were asked two questions: what is your age (x) and what do you believe is the age of the second oldest SNL host?

Note: the second oldest SNL guest host was Miskel Spillman at age 80 (in 1977) who won a contest and is the only non-celebrity to host the show.

X	25	29	32	37	40	45	47	50	53	60	65
Y	65	72	70	80	75	70	72	73	79	82	80

1. Draw a scatterplot for this set of data

2. Find the linear correlation coefficient. Based on that value, is there evidence of a linear relationship between the variables? Explain.

3. Find the line of best fit.

4. Predict the value of y given the value of x = 40

5. Find the residual for x = 40.

10. [5] Suppose that it can be shown that there is evidence of the following: There is a strong association between Betty White being a star on a show and Professor Simpson watching that show religiously.

Claim: By having Betty White star on a television show will guarantee Professor Simpson watches the show religiously.

What is the issue with this claim?

11. [6] While on Hot In Cleveland, Betty White was part of 2 live episodes. Not surprisingly, this increased her stress level. What about other actors? Stress scores follow a normal distribution with a mean of 3 and a standard deviation of 1.15. If a sample of 25 actors are taken, what is the probability that their average stress score is above 3.1?

Answer 1

Hi, We are supposed to answer one question at a time. Since you have not mentioned which question to answer. I am answering the first one. Please repost the remaining questions that you would like to be answered.

a) 95% Confidence interval

Following formula can be used to calculate the confidence Interval

The mean and standard deviation can be determined using excel:

The mean can determined using (=average) command:

The Standard deviation can be determined (=stdev.s) command:

The z score at 95% confidence level is 1.96

The confidence interval can be calculated as follows:

Test that whether average value is less than 23.7

Hypothesis test:

Step 1: Set up the hypothesis

Null Hypothesis: Ho: u = 23.7

Alternate Hypothesis:Ha: u < 23.7

Step 2: Decide the level of significance

The level of significance is assumed to be 0.05

Step 3: Calculate the test statistic

By referring to the standard normal table, the p-value at z = -4.248 is 0.0001

Conclusion:

Since the p value (0.0001) is less than the level of significance (0.05), teh null hypothesis will be rejected.

Therefore, there there is enough evidence to conclude that the number of shows are less than the average.

The type one error would that soap opera acting is harder than sitcom acting, but actually it is not.