Brand loyalty and the Chicago Cubs. According to literature on brand loyalty, consumers who are loyal to a brand are likely to consistently select the same product. This type of consistency could come from a positive childhood association. To examine brand loyalty among fans of the Chicago Cubs, 371 Cubs fans among patrons of a restaurant located in Wrigleyville were surveyed prior to a game at Wrigley Field, the Cubs’ home field.34 The respondents were classified as “die-hard fans” or “less loyal fans.” Of the 134 die-hard fans, 90.3% reported that they had watched or listened to Cubs games when they were children. Among the 237 less loyal fans, 67.9% said that they had watched or listened as children.

(a) Find the numbers of die-hard Cubs fans who watched or listened to games when they were children. Do the same for the less loyal fans.

(b) Use a significance test to compare the die-hard fans with the less loyal fans with respect to their childhood experiences relative to the team.

(c) Express the results with a 95% confidence interval for the difference in proportions.

Brand loyalty in action. The study mentioned
in the previous exercise found that two-thirds of the die-hard fans attended Cubs games at least once a month, but only 20% of the less loyal fans attended this often. Analyze these data using a significance test and a confidence interval. Write a short summary of your findings.

A sample of blood pressure measurements is taken from a data set and those values​ (mm Hg) are listed below. The values are matched so that subjects each have systolic and diastolic measurements. Find the mean and median for each of the two samples and then compare the two sets of results. Are the measures of center the best statistics to use with these​ data? What else might be​ better? ​Systolic: 150 126 95 140 154 159 145 101 152 135 ​Diastolic: 60 83 53 68 79 76 91 57 55 86 Find the means. The mean for systolic is nothing mm Hg and the mean for diastolic is nothing mm Hg. ​(Type integers or decimals rounded to one decimal place as​ needed.) Find the medians. The median for systolic is nothing mm Hg and the median for diastolic is nothing mm Hg. ​(Type integers or decimals rounded to one decimal place as​ needed.) Compare the results. Choose the correct answer below. A. The mean and median appear to be roughly the same for both types of blood pressure. B. The mean and the median for the systolic pressure are both lower than the mean and the median for the diastolic pressure. C. The mean and the median for the diastolic pressure are both lower than the mean and the median for the systolic pressure. D. The median is lower for the diastolic​ pressure, but the mean is lower for the systolic pressure. E. The mean is lower for the diastolic​ pressure, but the median is lower for the systolic pressure. Are the measures of center the best statistics to use with these​ data? A. Since the sample sizes are​ large, measures of center would not be a valid way to compare the data sets. B. Since the sample sizes are​ equal, measures of center are a valid way to compare the data sets. C. Since the systolic and diastolic blood pressures measure different​ characteristics, a comparison of the measures of center​ doesn't make sense. D. Since the systolic and diastolic blood pressures measure different​ characteristics, only measures of center should be used to compare the data sets. What else might be​ better? A. Since measures of center are​ appropriate, there would not be any better statistic to use in comparing the data sets. B. Because the data are​ matched, it would make more sense to investigate any outliers that do not fit the pattern of the other observations. C. Since measures of center would not be​ appropriate, it would make more sense to talk about the minimum and maximum values for each data set. D. Because the data are​ matched, it would make more sense to investigate whether there is an association or correlation between the two blood pressures.

I ran some test about something truly exciting and found that for Group A, the sample meanis 8.5, the standard deviationis 0.6, for n = 12. For Group B, the sample meanis 7.7, the standard deviationis 0.8, and n = 15. Use these values (which you will need to manipulate to suit your needs!) for #1-3. Yes, this is all the info you need!

1. Calculate the effect size using Cohen’s d.

2. Calculate the amount of variance accounted for using r².

3. Construct a 95% confidence interval to estimate the true difference between the groups. Is there one?

In this problem, assume that the distribution of differences is approximately normal. Note: For degrees of freedom d.f. not in the Student's t table, use the closest d.f. that is smaller. In some situations, this choice of d.f. may increase the P-value by a small amount and therefore produce a slightly more "conservative" answer. Suppose that at five weather stations on Trail Ridge Road in Rocky Mountain National Park, the peak wind gusts (in miles per hour) for January and April are recorded below. Wilderness District 1 2 3 4 5 January 133 122 134 64 78 April 110 97 107 88 61 Does this information indicate that the peak wind gusts are higher in January than in April? Use α = 0.01. Solve the problem using the critical region method of testing. (Let d = January − April. Round your answers to three decimal places.) test statistic = critical value =

You are still trying to estimate the girth of Kerrville toads. You collect 100 toads from many different ponds, rivers, witches cauldrons, etc around Kerrville. This is in the data set data("toad_girth") in my package. Using this data set find a 95% confidence interval for the population standard deviation of the toad girths:

In a study of the accuracy of fast food​ drive-through orders, one restaurant had 32 orders that were not accurate among 398 orders observed. Use a 0.10 significance level to test the claim that the rate of inaccurate orders is equal to​ 10%. Does the accuracy rate appear to be​ acceptable?

Identify the null and alternative hypotheses for this test. Choose the correct answer below.

A. H0​: p≠0.1 H1​: p=0.1

B. H0​: p=0.1 H1​: p≠0.1

C. H0​: p=0.1 H1​: p<0.1

D. H0​: p=0.1 H1​: p>0.1

Identify the test statistic for this hypothesis test.

The test statistic for this hypothesis test is _____ (Round to two decimal places as​ needed.)

Identify the​ P-value for this hypothesis test.

The​ P-value for this hypothesis test is _____ ​(Round to three decimal places as​ needed.)

Identify the conclusion for this hypothesis test.

A. Reject H0. There is not sufficient evidence to warrant rejection of the claim that the rate of inaccurate orders is equal to​ 10%.

B. Fail to reject H0. There is sufficient evidence to warrant rejection of the claim that the rate of inaccurate orders is equal to​ 10%.

C. Reject H0. There is sufficient evidence to warrant rejection of the claim that the rate of inaccurate orders is equal to​ 10%.

D. Fail to reject H0. There is not sufficient evidence to warrant rejection of the claim that the rate of inaccurate orders is equal to​ 10%.

Does the accuracy rate appear to be​ acceptable?

A. Since there is sufficient evidence to disprove the theory that the rate of inaccurate orders is equal to​ 10%, the accuracy rate is acceptable.

B. Since there is not sufficient evidence to disprove the theory that the rate of inaccurate orders is equal to​ 10%, it is possible that the accuracy rate is acceptable.

C. Since there is sufficient evidence to disprove the theory that the rate of inaccurate orders is equal to​ 10%, the accuracy rate is not acceptable. The restaurant should work to lower that rate.

D. Since there is not sufficient evidence to disprove the theory that the rate of inaccurate orders is equal to​ 10%, the accuracy rate is not acceptable. The restaurant should work to lower that rate

Paired sample test, (1) construct a 95% confidence interval and (2) conduct a t-test (α = 5%). This is to report to the NFL commisioner regarding points scored vs points allowed.

Data sets below

Team	Points Scored	Points Allowed
Los Angeles	463	429
Seattle	452	271
Indianapolis	439	247
New Orleans	435	398
NY Gants	422	314
Cincinnati	421	350
San Diego	418	312
Philadelphia	410	388
Kansas City	403	325
Tennessee	399	421
Green Bay	398	344
Denver	395	258
Carolina	391	259
Pittsburg	389	258
New England	379	338
Buffalo	371	367
Minnesota	366	344
Houston	365	431
Jacksonville	361	269
Washington	359	293
Atlanta	351	341
Arizona	342	387
Dallas	325	308
Miami	318	317
Tampa Bay	300	274
Oakland	290	383
Baltimore	265	299
Chicago	260	202
Detroit	254	345
NY Jets	240	355
San Francisco	239	228
Cleveland	232	301

The developers of a new online game have determined from preliminary testing that the scores of players on the first level of the game can be modelled satisfactorily by a Normal distribution with a mean of 185 points and a standard deviation of 28 points. They would like to vary the difficulty of the second level in this game, depending on the player’s score in the first level.

(a) The developers have decided to provide different versions of the second level for each of the following groups:

(i) those whose score on the first level is in the lowest 25% of scores

ii) those whose score on the first level is in the middle 50% of scores

(iii) those whose score on the first level is in the highest 25% of scores. Use the information given above to determine the cut-off scores for these groups. (You may round each of your answers to the nearest whole number.)

(b) In the second level of the game, the developers have also decided to give players an opportunity to qualify for a bonus round. Their stated aim is that players from group (i) should have 75% chance of qualifying for the bonus round, players from group (ii) should have 55% chance of qualifying for the bonus round and that players from group (iii) should have 30% chance of qualifying for this round. Let ?, ? and ? respectively denote the events that a player’s score on the first level was in the lowest 25% of scores, the middle 50% of scores and the highest 25% of scores, and let ? denote the event that the player qualifies for the bonus round. Use event notation to express the developers’ aim as a set of conditional probabilities.

(c) Based on the developers’ stated aim, find the total probability that a randomly chosen player will qualify for the bonus round.

(d) Given that a player has qualified for the bonus round, what is the probability that the player’s score on the first level was in the middle 50% of scores for that level?

(e) Given that a player has not qualified for the bonus round, what is the probability that the player’s score on the first level was in the lowest 25% of scores for that level?

Let X and Y be two independent random variables such that X + Y has the same density as X. What is Y?

A marketing researcher predicts that college students will be more likely to purchase tickets for... A marketing researcher predicts that college students will be more likely to purchase tickets for the next football home game if their team won (vs. lost) the last game. The researcher asked 6 WSU students their willingness to purchase tickets (1= not likely at all, 7=very likely) and 6 EWU students their willingness to purhcase tickets (1=not likely, 7=very likely) (WSU won the game in the 2018 season)

WSU: 7 6 5 7 2 4

EWU: 6 5 6 5 1 6

In answering the questions, make sure to write down the following 7 steps.

Step 1. Establish null and alternative hypotheses (as a sentance and formula)

Step 2: Calculate the degrees of freedom

Step 3: calculate the t-critical using critical t-table

Step 4: calculate the Sum of Squares deviation

Step 5: Calculate t-obtained

Step 6: Specify the critical value and the obtained value on a t-distribution curve.

A personnel specialist with a large accounting firm is interested in determining the effect of seniority on hourly wages for secretaries. She selects at random 10 secretaries and compares their years with the company (X) and hourly wages (Y).

x	y
0	12
2	13
3	14
6	16
5	15
3	14
4	13
1	12
1	15
2	15

• Calculate the regression slope and intercept (2 points).
• Predict the hourly wage of a secretary that has been with the company for four years (1 point).
• Find the coefficients of determination and nondetermination, and interpret both values (2 points).

A random sample of 200 books purchased at a local bookstore showed that 72 of the books were murder mysteries. Let p be the true proportion of books sold by this store that is murder mystery. Construct a confidence in terval with a 95% degree of confidence.Compute the following:

a.Point estimate

b.Critical value

c.Margin of error

d.Confidence interval

e.Interpretation(confidence statement).

What is your favorite color? A large survey of countries, including the United States, China, Russia, France, Turkey, Kenya, and others, indicated that most people prefer the color blue. In fact, about 24% of the population claim blue as their favorite color.† Suppose a random sample of n = 54 college students were surveyed and r = 11 of them said that blue is their favorite color. Does this information imply that the color preference of all college students is different (either way) from that of the general population? Use α = 0.05. (a) What is the level of significance? 0.05 Correct: Your answer is correct. State the null and alternate hypotheses. H0: p = 0.24; H1: p > 0.24 H0: p = 0.24; H1: p ≠ 0.24 H0: p ≠ 0.24; H1: p = 0.24 H0: p = 0.24; H1: p < 0.24 Correct: Your answer is correct. (b) What sampling distribution will you use? The Student's t, since np > 5 and nq > 5. The standard normal, since np < 5 and nq < 5. The Student's t, since np < 5 and nq < 5. The standard normal, since np > 5 and nq > 5. Correct: Your answer is correct. What is the value of the sample test statistic? (Round your answer to two decimal places.) -0.04 Incorrect: Your answer is incorrect. (c) Find the P-value of the test statistic. (Round your answer to four decimal places.) 0.24 Incorrect: Your answer is incorrect.

Researchers watched groups of dolphins off the coast of Ireland in 1998 to determine what activities the dolphins partake in at certain times of the day ("Activities of dolphin," 2013). The numbers in Table 3 represent the number of groups of dolphins that were partaking in an activity at certain times of days. Is there enough evidence to show that the activity and the time period are independent for dolphins? Why or Why not? Test at the 1% level.

Activity	Morning	Noon	Afternoon	Evening	Row Total
Travel	6	6	14	13	39
Feed	28	4	0	56	88
Social	38	5	9	10	62
Column Total	72	15	23	79	189

In 2003 and 2017 a poll asked Democratic voters about their views on the FBI. In​ 2003, 42​% thought the FBI did a good or excellent job. In​ 2017, 64​% of Democratic voters felt this way. Assume these percentages are based on samples of 1200 Democratic voters.

1) Can we​ conclude, on the basis of these two percentages​ alone, that the proportion of Democratic voters who think the FBI is doing a good or excellent job has increased from 2003 to​ 2017? Why or why​ not?

Select one:

a. No. Although a lesser percentage is present in the​ sample, the population percentages could be the same or even reversed.

b. No. Since a greater percentage is present in the​ sample, we cannot conclude that a lesser percentage of Democratic voters who think the FBI is doing a good or excellent job is present in the population.

c. No. Although a lesser percentage is present in the​ sample, the population percentages could be the​ same, but could not be reversed.

d. Yes. Since a lesser percentage is present in the​ sample, a lesser percentage of Democratic voters who think the FBI is doing a good or excellent job is present in the population.

2) Construct a 95​% confidence interval for the difference in the proportions of Democratic voters who believe the FBI is doing a good or excellent​ job, p1−p2. Let p1 be the proportion of Democratic voters who felt this way in 2003 and p2 be the proportion of Democratic voters who felt this way in 2017.

Select one:

a. (0.39, 0.45)

b. (-0.259, -0.181)

c. (-0.24, -0.20)

d. (0.63, 0.65)