Modern medical practice tells us not to encourage babies to become too fat. Is there a positive correlation between the weight, x, or a 1-year-old baby and the weight, y, of the mature adult (30 years old)? A random sample of medical files produced the following information for 14 females. Please use this data to answer all parts of the question.

x (lbs) 21 25 23 24 20 15 25 21 17 24 26 22 18 19

y (lbs) 125 125 120 125 130 120 145 130 130 130 130 140 110 115

note: For these data, ?̅≈ 21.42, ?? ≈ 3.32, ?̅ ≈ 126.79, ?? ≈ 9.12 1.

Use a 5% level of significance to test the claim that ? > 0.

a. State the null and alternative hypotheses.

?0:

?1:

b. What calculator test will you use? List the requirements that must be met for you to use this test, and indicate whether the conditions are met in this problem.

c. Run the calculator test and obtain the P-value.

d. Based on your P-value, will you reject or fail to reject the null hypothesis?

e. Interpret your conclusion from part d in the context of this problem. In other words, what does this result tell you about the population correlation between the weight of a child at 1 year, and their corresponding weight as an adult?

Explain what an influential multivariate outlier is, and at least two methods of coping with them in multiple regression.

Discuss two approaches to using multiple regression when the assumption of multivariate normality is violated.

Using the appropriate model, sample size n, and output below: Model: y = β0 + β1x1 + β2x2 + β3x3 + ε Sample size: n = 16 Regression Statistics Multiple R .9979 R Square .9958 Adjusted R Square .9947 Standard Error 403.4885 Observations 16 ANOVA DF SS MS F Significance F Regression 3 462,169,641.8709 154,056,547.2903 946.2760 .0000 Residual 12 1,953,635.6197 162,802.9683 Total 15 464,123,277.4907 (1) Report SSE, s2, and s as shown on the output. (Round your answers to 4 decimal places.) SSE s2 s (2) Report R2 and R⎯⎯⎯2 as shown on the output. (Round your answers to 4 decimal places.) R2 Picture (3) Report the total variation, unexplained variation, and explained variation as shown on the output. (Round your answers to 4 decimal places.) Total variation Unexplained variation Explained variation (4) Calculate the F(model) statistic by using the explained variation, the unexplained variation, and other relevant quantities. (Round your answer to 3 decimal places.) F(model) (5) Use the F(model) statistic and the appropriate rejection point to test the significance of the linear regression model under consideration by setting α equal to .05. H0: β1 = β2 = β3 = 0 by setting α = .05. (6) Use the F(model) statistic and the appropriate rejection point to test the significance of the linear regression model under consideration by setting α equal to .01. H0: β1 = β2 = β3 = 0 by setting α = .01. (7) Find the p-value related to F(model) on the output. Using the p-value, test the significance of the linear regression model by setting α = .10, .05, .01, and .001. p-value = .000. H0 at α = .05, .01, and .001.

Businesses know that customers often respond to background music. Do they also respond to odors? One study of this question took place in a small pizza restaurant in France on two Saturday evenings in May. On one of these evenings, a relaxing lavender odor was spread through the restaurant. On the other evening no scent was used. The data gives the time, in minutes, that two samples of 30 customers spent in the restaurant and the amount they spent in euros. No odor Lavender Minutes Euros spent Minutes Euros spent 103 15.9 92 21.9 68 18.5 126 18.5 79 15.9 114 22.3 106 18.5 106 21.9 72 18.5 89 18.5 121 21.9 137 24.9 92 15.9 93 18.5 84 15.9 76 22.5 72 15.9 98 21.5 92 15.9 108 21.9 85 15.9 124 21.5 69 18.5 105 18.5 73 18.5 129 25.5 87 18.5 103 18.5 109 20.5 107 18.5 115 18.5 109 21.9 91 18.5 94 18.5 84 15.9 105 18.5 76 15.9 102 24.9 96 15.9 108 21.9 107 18.5 95 25.9 98 18.5 121 21.9 92 15.9 109 18.5 107 18.5 104 18.5 93 15.9 116 22.8 118 18.5 88 18.5 87 15.9 109 21.9 101 25.5 97 20.7 75 12.9 101 21.9 86 15.9 106 22.5 To access the complete data set, click the link for your preferred software format: Excel Minitab JMP SPSS TI R Mac-TXT PC-TXT CSV CrunchIt! The two evenings were comparable in many ways (weather, customer count, and so on), so we are willing to regard the data as independent SRSs from spring Saturday evenings at this restaurant. The authors say, "Therefore, at this stage it would be impossible to generalize the results to other restaurants." (a) Does a lavender odor encourage customers to stay longer in the restaurant? Examine the time data and explain why they are suitable for two‑sample ? procedures. Because the distributions are reasonably symmetric with no outliers and the samples can be treated as independent SRSs, the ? procedures will work well. false true Let ?1 be the population mean time in the restaurant with no scent, and ?2 be the mean time with a lavender odor. State the null and alternative hypotheses. ?0:?1=?2 vs. ??:?1>?2 ?0:?1=?2 vs. ??:?1<?2 ?0:?1>?2 vs. ??:?1<?2 ?0:?1=?2 vs. ??:?1≠?2 Give the value of the test statistic. (Enter your answer rounded to two decimal places.) test statistic: Use the conservative degrees of freedom to give the P‑value for the test. 0.01<?<0.02 0.0005<?<0.001 ?<0.0005 0.0025<?<0.005 What is your conclusion? We have sufficient evidence that customers stay longer when there is no odor. There is no evidence that the mean time spent in the restaurant when lavender odor is present is different from the mean time spent when there is no odor. We have some evidence that the mean times spent when lavender odor is present and when there is no odor are not the same. We have strong evidence that customers stay longer when the lavender odor is present. (b) Does a lavender odor encourage customers to spend more while in the restaurant? Examine the spending data. In what ways do these data deviate from normality? Select your choices. There are extreme outliers. The distributions do not have similar shapes. The distributions are skewed and have many gaps. There are two clear asymmetrical peaks in each distribution. If ?1 is the population mean spending with no scent, and ?2 is the mean spending with a lavender odor, what are the null and alternative hypotheses? ?0:?1=?2 versus ??:?1<?2 ?0:?1−?2=0 versus ??:?1−?2>0 ?0:?1=?2 versus ??:?1≠?2 ?0:?1=?2 versus ??:?1>?2 Give the value of the test statistic. (Enter your answer rounded to two decimal places.) test statistic: What is the P‑value? ?<0.0005 0.0025<?<0.005 0.0005<?<0.001 0.01<?<0.02 What is your conclusion? We have strong evidence that customers spend more when the lavender odor is present. We have some evidence that mean spending is larger when the lavender odor is present. We have strong evidence that the presence of lavender odor has no effect on the spendings of customers. The data is not sufficient to give evidence against the null hypothesis of no difference in spendings.

Test the given claim. Identify the null​ hypothesis, alternative​ hypothesis, test​ statistic, P-value, and then state the conclusion about the null​ hypothesis, as well as the final conclusion that addresses the original claim. Among 2158 passenger cars in a particular​ region, 235 had only rear license plates. Among 351 commercial​ trucks, 49 had only rear license plates. A reasonable hypothesis is that commercial trucks owners violate laws requiring front license plates at a higher rate than owners of passenger cars. Use a 0.01 significance level to test that hypothesis. a. Test the claim using a hypothesis test. b. Test the claim by constructing an appropriate confidence interval. a. Identify the null and alternative hypotheses for this test. Let population 1 correspond to the passenger cars and population 2 correspond to the commercial trucks . Let a success be a vehicle that only has a rear license plate. A. Upper H 0 ​: p 1 equalsp 2Upper H 1 ​: p 1 greater thanp 2 B. Upper H 0 ​: p 1 equalsp 2Upper H 1 ​: p 1 not equalsp 2 C. Upper H 0 ​: p 1 less thanp 2Upper H 1 ​: p 1 equalsp 2 D. Upper H 0 ​: p 1 equalsp 2Upper H 1 ​: p 1 less thanp 2 Identify the test statistic. nothing ​(Round to two decimal places as​ needed.) Identify the​ P-value. nothing ​(Round to three decimal places as​ needed.) State the conclusion about the null​ hypothesis, as well as the final conclusion that addresses the original claim. A. Reject Upper H 0 . There is not sufficient evidence to support the claim that commercial trucks owners violate laws requiring front license plates at a higher rate than owners of passenger cars. B. Fail to reject Upper H 0 . There is sufficient evidence to support the claim that commercial trucks owners violate laws requiring front license plates at a higher rate than owners of passenger cars. C. Reject Upper H 0 . There is sufficient evidence to support the claim that commercial trucks owners violate laws requiring front license plates at a higher rate than owners of passenger cars. D. Fail to reject Upper H 0 . There is not sufficient evidence to support the claim that commercial trucks owners violate laws requiring front license plates at a higher rate than owners of passenger cars. b. Identify the confidence interval limits for the appropriate confidence interval. Let population 1 correspond to the passenger cars and population 2 correspond to the commercial trucks . Let a success be a vehicle that only has a rear license plate. nothing less thanp 1minusp 2less thannothing ​(Round to four decimal places as​ needed.) Because the confidence interval limits ▼ contain do not contain ​0, there ▼ is not is a significant difference between the two proportions. There ▼ is is not sufficient evidence to support the claim that commercial trucks owners violate laws requiring front license plates at a higher rate than owners of passenger cars. Click to select your answer(s).

In a large clinical​ trial, 395 comma 679 children were randomly assigned to two groups. The treatment group consisted of 197 comma 927 children given a vaccine for a certain​ disease, and 36 of those children developed the disease. The other 197 comma 752 children were given a​ placebo, and 135 of those children developed the disease. Consider the vaccine treatment group to be the first sample. Complete parts​ (a) through​ (d) below. a. Assume that a 0.01 significance level will be used to test the claim that p 1 less thanp 2 . Which is​ better: A hypothesis test or a confidence​ interval? ▼ A confidence interval A hypothesis test is better. b. In​ general, when dealing with inferences for two population​ proportions, which two of the following are​ equivalent: confidence interval​ method; P-value​ method; critical value​ method? ▼ Confidence interval method and Upper P dash value method Confidence interval method and critical value method Upper P dash value method and critical value method are​ equivalent, in that they will always lead to the same conclusion. Both of these methods use a standard deviation based on ▼ the assumption that the two population proportions are equal, estimated values of the population proportions, whereas the other method uses a standard deviation based on ▼ estimated values of the population proportions. the assumption that the two population proportions are equal. c. If a 0.01 significance level is to be used to test the claim that p 1 less thanp 2 ​, what confidence level should be​ used? nothing ​% ​(Type an integer or a​ decimal.) d. If the claim in part​ (c) is tested using this sample​ data, we get this confidence​ interval: negative 0.000655 less thanp 1minusp 2less thannegative 0.000347 . What does this confidence interval suggest about the​ claim? Because the confidence interval ▼ contains does not contain ▼ 0, the critical value, the pooled sample proportion, the significance level, there ▼ appears to be does not appear to be a significant difference between the two proportions. Because the confidence interval consists ▼ only of values greater than of values both less than and greater than only of values less than ▼ the pooled sample proportion, the significance level, 0, the critical value, it appears that the first proportion is ▼ less than greater than not significantly different from the second proportion. There is ▼ insufficient sufficient evidence to support the claim that the rate of polio is less for children given the vaccine than it is for children given a placebo. Enter your answer in the answer box.

Question 2 [25]
UNAM Alumni Office sample of 250 alumnus to find out if they were employed in one years after completion of their studies and results were as follows 75= Yes responses, 175= No Responses
Compute the following for alumnus who responded Yes.
a) The Margin of error at 90% confidence level [6]
b) 90% confidence interval [4]
c) The Margin of error at 95% confidence level [6]
d) 95% confidence interval [4]

Page 10 of 13

e) The size of sample should be taken with a 0.90 probability, if the desired margin of error is 2% [5]

Is the number of games won by a major league baseball team in a season related to the team batting average? The table below shows the number of games won and the batting average (in thousandths) of 8 teams.

Using games won as the explanatory variable x, do the following:

(a) The correlation coefficient is r=  .

(b) The equation of the least squares line is y^=

Question 1 [25]
Namibia Car Dealers wants to determine the number of defects per new car. Suppose you are asked to conduct the quality survey for cars, suppose you sampled 30 new cars and following data on number of defects per car were recorded.
0 1 1 2 1 0 2 3 2 1 0 4 3 1 1 0 2 0 0 2 3 0 2 0 2 0 3 1 0 2 a) Compute the sample mean number of defects per car [2] b) Compute the sample standard deviation [5] c) Compute the standard error of mean, assuming that ?̅ and s are equal to ? and ? respectively [2] d) Compute the probability that number of defects per car more than 1.5 [5] e) Draw the distribution in d. [3] f) Compute the probability that that number of defects per is between 1 and 2 [5] g) Draw the distribution in d. [3] vQuestion 1 [25]
Namibia Car Dealers wants to determine the number of defects per new car. Suppose you are asked to conduct the quality survey for cars, suppose you sampled 30 new cars and following data on number of defects per car were recorded.
0 1 1 2 1 0 2 3 2 1 0 4 3 1 1 0 2 0 0 2 3 0 2 0 2 0 3 1 0 2 a) Compute the sample mean number of defects per car [2] b) Compute the sample standard deviation [5] c) Compute the standard error of mean, assuming that ?̅ and s are equal to ? and ? respectively [2] d) Compute the probability that number of defects per car more than 1.5 [5] e) Draw the distribution in d. [3] f) Compute the probability that that number of defects per is between 1 and 2 [5] g) Draw the distribution in d. [3] vQuestion 1 [25]
Namibia Car Dealers wants to determine the number of defects per new car. Suppose you are asked to conduct the quality survey for cars, suppose you sampled 30 new cars and following data on number of defects per car were recorded.
0 1 1 2 1 0 2 3 2 1 0 4 3 1 1 0 2 0 0 2 3 0 2 0 2 0 3 1 0 2 a) Compute the sample mean number of defects per car [2] b) Compute the sample standard deviation [5] c) Compute the standard error of mean, assuming that ?̅ and s are equal to ? and ? respectively [2] d) Compute the probability that number of defects per car more than 1.5 [5] e) Draw the distribution in d. [3] f) Compute the probability that that number of defects per is between 1 and 2 [5] g) Draw the distribution in d. [3] vQuestion 1 [25]
Namibia Car Dealers wants to determine the number of defects per new car. Suppose you are asked to conduct the quality survey for cars, suppose you sampled 30 new cars and following data on number of defects per car were recorded.
0 1 1 2 1 0 2 3 2 1 0 4 3 1 1 0 2 0 0 2 3 0 2 0 2 0 3 1 0 2 a) Compute the sample mean number of defects per car [2] b) Compute the sample standard deviation [5] c) Compute the standard error of mean, assuming that ?̅ and s are equal to ? and ? respectively [2] d) Compute the probability that number of defects per car more than 1.5 [5] e) Draw the distribution in d. [3] f) Compute the probability that that number of defects per is between 1 and 2 [5] g) Draw the distribution in d. [3] Question 1 [25]
Namibia Car Dealers wants to determine the number of defects per new car. Suppose you are asked to conduct the quality survey for cars, suppose you sampled 30 new cars and following data on number of defects per car were recorded.
0 1 1 2 1 0 2 3 2 1 0 4 3 1 1 0 2 0 0 2 3 0 2 0 2 0 3 1 0 2 a) Compute the sample mean number of defects per car [2] b) Compute the sample standard deviation [5] c) Compute the standard error of mean, assuming that ?̅ and s are equal to ? and ? respectively [2] d) Compute the probability that number of defects per car more than 1.5 [5] e) Draw the distribution in d. [3] f) Compute the probability that that number of defects per is between 1 and 2 [5] g) Draw the distribution in d. [3] Question 1 [25]
Namibia Car Dealers wants to determine the number of defects per new car. Suppose you are asked to conduct the quality survey for cars, suppose you sampled 30 new cars and following data on number of defects per car were recorded.
0 1 1 2 1 0 2 3 2 1 0 4 3 1 1 0 2 0 0 2 3 0 2 0 2 0 3 1 0 2 a) Compute the sample mean number of defects per car [2] b) Compute the sample standard deviation [5] c) Compute the standard error of mean, assuming that ?̅ and s are equal to ? and ? respectively [2] d) Compute the probability that number of defects per car more than 1.5 [5] e) Draw the distribution in d. [3] f) Compute the probability that that number of defects per is between 1 and 2 [5] g) Draw the distribution in d. [3]

When answering a question on a multiple choice exam, Jon either thinks he knows the answer or just guesses.

Suppose the probability that Jon thinks he knows the answer is 0.75 and there’s a 90% chance that he’ll get the question correct if he thinks he knows the answer. There are 5 choices for each multiple-choice exam question.

Each question is worth 2 marks (no part marks), but blank answers earn 0.4 marks. Suppose Jon always answers the question if he thinks he knows the answer, but if he does not, he guesses the answer (at random) half the time and the other half of the time, he leaves the answer blank.

What is the expected value of Jon’s score on a randomly selected question?

Problem 9-07 (Algorithmic) As part of the settlement for a class action lawsuit, Hoxworth Corporation must provide sufficient cash to make the following annual payments (in thousands of dollars): Year 1 2 3 4 5 6 Payment 195 220 270 320 350 470 The annual payments must be made at the beginning of each year. The judge will approve an amount that, along with earnings on its investment, will cover the annual payments. Investment of the funds will be limited to savings (at 3.5% annually) and government securities, at prices and rates currently quoted in The Wall Street Journal. Hoxworth wants to develop a plan for making the annual payments by investing in the following securities (par value = $1000). Funds not invested in these securities will be placed in savings. Security Current Price Rate (%) Years to Maturity 1 $1045 6.85 3 2 $1000 5.525 4 Assume that interest is paid annually. The plan will be submitted to the judge and, if approved, Hoxworth will be required to pay a trustee the amount that will be required to fund the plan. Use linear programming to find the minimum cash settlement necessary to fund the annual payments. Let F = total funds required to meet the six years of payments G1 = units of government security 1 G2 = units of government security 2 Si = investment in savings at the beginning of year i Note: All decision variables are expressed in thousands of dollars. If required, round your answers to five decimal places. For subtractive or negative numbers use a minus sign even if there is a + sign before the blank. (Example: -300) Min F s.t. F + G1 + G2 + S1 = G1 + G2 + S1 + S2 = G1 + G2 + S2 + S3 = G1 + G2 + S3 + S4 = G2 + S4 + S5 = S5 + S6 = Round your answer to the nearest dollar. If an amount is zero, enter "0". Current investment required $ Investment in government security 1 $ Investment in government security 2 $ Investment in savings for year 1 $ Investment in savings for year 2 $ Investment in savings for year 3 $ Investment in savings for year 4 $ Investment in savings for year 5 $ Investment in savings for year 6 $ Use the dual value to determine how much more Hoxworth should be willing to pay now to reduce the payment at the beginning of year 6 to $400,000. Round your answer to the nearest dollar. $ Use the dual value to determine how much more Hoxworth should be willing to pay to reduce the year 1 payment to $150,000. Round your answer to the nearest dollar. Hoxworth should be willing to pay anything less than $ . Suppose that the annual payments are to be made at the end of each year. Reformulate the model to accommodate this change. Note: All decision variables are expressed in thousands of dollars. If required, round your answers to five decimal places. For subtractive or negative numbers use a minus sign even if there is a + sign before the blank. (Example: -300) Min F s.t. 1) F + G1 + G2 + S1 = 2) G1 + G2 + S1 + S2 = 3) G1 + G2 + S2 + S3 = 4) G1 + G2 + S3 + S4 = 5) G2 + S4 + S5 = 6) S5 + S6 = 7) S6 + S7 = How much would Hoxworth save if this change could be negotiated? Round your answer to the nearest dollar. $ PreviousNext

A medical test has been designed to detect the presence of a certain disease. Among people who have the disease, the probability that the disease will be detected by the test is 0.93. However, the probability that the test will erroneously indicate the presence of the disease in those who do not actually have it is 0.03. It is estimated that 3% of the population who take this test have the disease. (Round your answers to three decimal places.)

(a) If the test administered to an individual is positive, what is the probability that the person actually has the disease?


(b) If an individual takes the test twice and the test is positive both times, what is the probability that the person actually has the disease? (Assume that the tests are independent.)

In a Survey respondents were asked whether or not they had a Facebook account. Of men 215 men, 70 had an active facebook profile, while 347 had 85 active profiles. Given that facebook has had an approximately 50 million users.

A) Are these two population dependent or independent? Explain

B)Find the point estimate for each population rounded to two decimals.

C) Can we say that this is normally distributed data? why?

D) Are there more males than females on facebook? Construct and interpret an alpha .1 hypothesis test.

A random sample of 160 car purchases are selected and categorized by age. The results are listed below. The age distribution of drivers for the given categories is 18% for the under 26 group, 39% for the 26-45 group, 31% for the 45-65 group, and 12% for the group over 65. Find the P-value to test the claim that all ages have purchase rates proportional to their driving rates. Use α = 0.05.

please explain how to solve problem on the ti84 calculator. please also explain how you got the answer without the calculator.

ANSWERS

A) 0.01 < P < 0.025

B) P > 0.10

C) P < 0.005

D) 0.005 < P < 0.01