Membership selection. A town council has 13 ​members, 7 Democrats and 6 Republicans.

A nutrition consulting company created an education program to increase the calcium intake in children ages 9 to 13. To measure the effectiveness of the program, an analyst performs an experiment in which 198 children are assigned randomly to either the control group (no education) or the education group. The average daily dietary calcium intake is calculated from 3-day diet records. Before the analyst can perform hypothesis tests, she needs to know if the variances of the two groups are equal or not so that she can determine what type of hypothesis test to use (Parametric or Non-Parametric). Use the Equal_Variances.MTW data file to perform a test of equal variances and determine if the two groups have equal variances.

Calcium   Group
646.718938358203   Control
1120.66884477362   Control
1067.25197943551   Control
911.624742599909   Control
898.895367854688   Control
1088.41268757664   Control
1271.48521000362   Control
729.383778742021   Control
983.859574875372   Control
905.044576198034   Control
546.071919866484   Control
715.568075723858   Control
966.077942357849   Control
1099.84663143188   Control
1035.60968971358   Control
698.565902695813   Control
935.751007584594   Control
865.305220486097   Control
1232.5438640389   Control
899.699184074123   Control
1259.54465321706   Control
1327.13626005019   Control
954.862824311777   Control
683.096757798792   Control
839.797920019532   Control
608.791819237845   Control
1063.60241792683   Control
1287.18586964095   Control
910.147706316883   Control
1049.07762406466   Control
336.23327683719   Control
520.921030893244   Control
807.353805936021   Control
1429.69059848441   Control
461.065913514199   Control
954.824551355506   Control
359.473499314655   Control
1150.06303841653   Control
722.74667000439   Control
1069.23255942596   Control
883.213304316289   Control
829.472760293924   Control
1341.87329441388   Control
567.274109385454   Control
702.367646659113   Control
872.716285426422   Control
320.781003645417   Control
788.717898193134   Control
795.270919272801   Control
1174.45273674766   Control
684.286947645718   Control
1197.97911103269   Control
871.59081913733   Control
558.624799529507   Control
682.764196350705   Control
425.366614281267   Control
364.69994726096   Control
502.306961956663   Control
1010.01657543712   Control
721.851178257459   Control
783.754839352849   Control
941.094730484834   Control
681.53021550534   Control
714.32289464054   Control
546.596093290559   Control
701.966170386693   Control
407.506044392304   Control
649.724734020368   Control
1013.90578437461   Control
487.251009881645   Control
1125.02859624156   Control
801.070963955146   Control
913.505590201886   Control
555.303404529004   Control
626.344387491074   Control
1118.94696799092   Control
800.133615896361   Control
817.559677766571   Control
677.293702889565   Control
577.136195347531   Control
797.011616506485   Control
574.405945643188   Control
673.860788692258   Control
640.154335629558   Control
726.754006577547   Control
871.837981179152   Control
554.916353340325   Control
817.765305093996   Control
1023.53922905079   Control
778.440001362496   Control
1033.75166394017   Control
863.072814876006   Control
482.929204765678   Control
757.717697206004   Control
961.759393491617   Control
752.079104746515   Control
1099.64642788733   Control
675.889347527723   Control
1212.86127908923   Education
1043.58183576511   Education
1001.02467542113   Education
1433.66666503496   Education
1242.36295439191   Education
1005.38027642987   Education
1310.90065971212   Education
1041.10713152717   Education
1039.0993753776   Education
989.203765312553   Education
1152.30889717592   Education
1069.27412733254   Education
1222.95571155341   Education
937.227131758598   Education
1231.97180255013   Education
1288.30956894443   Education
934.641799963676   Education
951.519397164352   Education
880.150953760751   Education
1337.12934460539   Education
1150.20746167798   Education
1425.89368404825   Education
1107.11421120659   Education
1347.23302140043   Education
1057.36151355459   Education
807.630671558523   Education
1393.46121505187   Education
1265.1805592468   Education
974.043747071429   Education
1043.12557050404   Education
1101.07770090962   Education
1100.36253237378   Education
1269.85555459434   Education
1117.16284246044   Education
1273.25093388539   Education
918.442747376225   Education
1154.10000749998   Education
1031.95095005953   Education
1196.46758876627   Education
1167.80704978808   Education
652.41252737704   Education
705.073189240597   Education
1160.07605005674   Education
1215.92689429818   Education
1269.67988395412   Education
992.532061947513   Education
893.230651173659   Education
1040.01683270812   Education
998.869581034692   Education
1292.45533515759   Education
985.769272826702   Education
1062.04422672555   Education
913.108875584995   Education
907.570870445983   Education
1155.11840910918   Education
1517.17232610728   Education
982.892509295403   Education
1033.85082546014   Education
1298.96779458962   Education
713.114373419194   Education
751.241491805589   Education
1254.81650540777   Education
1168.4696785167   Education
939.693919974494   Education
1167.76178576134   Education
1190.6386610843   Education
1040.1220559694   Education
1502.88356884033   Education
1128.50289428548   Education
1034.90807572673   Education
1188.42295410829   Education
1291.87796136998   Education
1279.34817295133   Education
1283.98058261949   Education
1022.57252075428   Education
1117.19876078909   Education
931.503937304133   Education
1233.74375961551   Education
1469.41522092619   Education
716.816245140364   Education
1052.92091190376   Education
1347.81770450501   Education
1371.16163167695   Education
1081.63622765917   Education
961.941039301563   Education
1433.1882590068   Education
1241.81563105457   Education
1060.29846142643   Education
1011.40603523059   Education
1153.07766725887   Education
963.551933580363   Education
1082.42275789195   Education
1057.30148554377   Education
1321.56941906484   Education
766.866676879017   Education
1117.46167012446   Education
934.032532507596   Education
1309.17920918181   Education
1284.76821777109   Education
993.098270535973   Education

Suppose the event of a student’s application to a university being accepted follows the binomial probability and the successful rate is 80%. Please finish the following tasks? (1) Determine the expected number of acceptances for the next 7 applicants and the standard deviation. (2) What is the probability that among the next 9 applicants exactly 5 will be accepted?

In the Focus Problem at the beginning of this chapter, a study was described comparing the hatch ratios of wood duck nesting boxes. Group I nesting boxes were well separated from each other and well hidden by available brush. There were a total of 485 eggs in group I boxes, of which a field count showed about 276 hatched. Group II nesting boxes were placed in highly visible locations and grouped closely together. There were a total of 780 eggs in group II boxes, of which a field count showed about 270 hatched.

(a) Find a point estimate p̂₁ for p₁, the proportion of eggs that hatch in group I nest box placements. (Round your answer to three decimal places.)
p̂₁ =

Find a 99% confidence interval for p₁. (Round your answers to three decimal places.)

(b) Find a point estimate p̂₂ for p₂, the proportion of eggs that hatch in group II nest box placements. (Round your answer to three decimal places.)
p̂₂ =

Find a 99% confidence interval for p₂. (Round your answers to three decimal places.)

(c) Find a 99% confidence interval for p₁ − p₂. (Round your answers to three decimal places.)

Does the interval indicate that the proportion of eggs hatched from group I nest boxes is higher than, lower than, or equal to the proportion of eggs hatched from group II nest boxes?

Because the interval contains only negative numbers, we can say that a higher proportion of eggs hatched in highly visible, closely grouped nesting boxes.Because the interval contains both positive and negative numbers, we can not say that a higher proportion of eggs hatched in well-separated and well-hidden nesting boxes.    We can not make any conclusions using this confidence interval.Because the interval contains only positive numbers, we can say that a higher proportion of eggs hatched in well-separated and well-hidden nesting boxes.

(d) What conclusions about placement of nest boxes can be drawn? In the article discussed in the Focus Problem, additional concerns are raised about the higher cost of placing and maintaining group I nest box placements. Also at issue is the cost efficiency per successful wood duck hatch.

No conclusion can be made.A greater proportion of wood duck eggs hatch if the eggs are laid in well-separated, well-hidden nesting boxes.    The eggs hatch equally well in both conditions.A greater proportion of wood duck eggs hatch if the eggs are laid in highly visible, closely grouped nesting boxes.

James travels from Toronto to Calgary then Vancouver and finally to Prince George. There is a 5% chance that his luggage is left behind in Toronto. If it is not left behind in Toronto, there is a 7% chance that it is left behind in Calgary. If it not left behind in Toronto or Calgary, there is a 10% chance that it is left behind in Vancouver. What is the probability his luggage is lost?

A researcher wants to study the effectiveness of medication and the time of day on alertness. 18 patients are randomly selected and three are assigned to each of six groups. Their alertness scores are listed on the table. Is there any difference in the mean score depending on 1) the type of treatment, 2) time, and 3) an interaction effect between treatment and time? Use an alpha level of .05.

Provide Formula for answers, Excel is not allowed.

Match the described probability with the type of probability.

Six months before its annual convention, the American Medical Association must determine how many rooms to reserve. At this time, the AMA can reserve rooms at a cost of $50 per room. All rooms that are reserved must be paid for even if they are not used. The AMA believes the number of doctors attending the convention will be normally distributed with a mean of 5000 and a standard deviation of 1000. If the number of people attending the convention exceeds the number of rooms reserved, extra rooms must be acquired at a cost of $80 per room. Use a simulation model to determine the expected cost of the rooms for the convention for the following reservation levels: 2000, 3000, 4000, 5000, 6000, 7000, and 8000. From the above list of reservation levels, select the optimal number of rooms to reserve. Use a simulation with 2000 replicates and answer the questions below:

a) What is the optimal number of rooms to reserve?  (Click to select)  2000  3000  4000  5000  6000  7000  8000

(Round the following answers to two decimals)

b) What is the expected minimum cost? $

b) Construct a 95% confidence interval for the expected cost for the optimal number of rooms to reserve:

3. Estimate Interval The makers of a soft drink want to identify the average age of its consumers. A sample of 61 consumers was taken. The average age in the sample was 23 years with a sample standard deviation of 5 years. Please answer the following questions: a. Construct a 95% confidence interval estimate for the mean of the consumers’ age. b. Suppose a sample of 85 was selected (with the same mean and the sample standard deviation). Construct a 95% confidence interval for the mean of the consumers’ age.

[Hint: Please see Chap008 – Slides 24-29 for formula and example. Please also see page 343-349 in the textbook.]

4. Hypothesis Testing Annual per captial consumption of milk is 21.6 gallons (Statistical Abstract of the United States: 2006). Being from the Midwest, you believe milk consumption is higher there and wish to support your opinion. A sample of 16 individuals from the Midwestern town of Webster City showed a sample mean annual consumption of 24.1 gallons with a sample standard deviation of s=4.8. a. Develop a hypothesis test that can be used to determine whether the mean annual consumption in Webster City is higher than the national mean. b. At α=0.05, test for a significant difference. What is your conclusion? Extra credit 5. A lathe is set to cut bars of steel into lengths of 9 centimeters. The lathe is considered to be in perfect adjustment if the average length of the bars it cuts is 9 centimeters. A sample of 100 bars is selected randomly and measured. It is determined that the average length of the bars in the sample is 9.085 centimeters. Suppose the population standard deviation is 0.335 centimeters. a. Formulate the hypotheses to determine whether or not the lathe is in perfect adjustment. b. Compute the test statistic. c. Using the p-value approach, what is your conclusion? Let α = .05.

The mileage of the hybrid car, the Honda Insight, is normally distributed with a mean of 63.4 mpg and a standard deviation of 12.6 mpg.

1. Is it possible to find the probability that the mean mileage of seven Honda Insights exceeds 70 mpg? Provide a justification for your answer.

2. If we want to address the problem “Find the probability that the mean mileage of seven Honda Insights exceeds 70 mpg”, write the probability statement.

3. If we want to address the problem “Find the probability that the mean mileage of seven Honda Insights exceeds 70 mpg”, what is the probability? Be sure to show how you calculated your probability.

This example was previously posted, but how did we come up with a Q1 result of 28.5 and a Q3 result of 123.3 for the question below? I am wondering where I went wrong here, as the results to this question have already been posted. The results I have are Q1 of 29 and Q3 of 121 with a median of 69. I have IQR as 92 and for outliers I have -109 for lower limit and 259 for upper limit. I am wondering how we came up with 28.5 for Q1 and 123.3 for Q3. Once I understand this, then figuring out IQR and outlier limits makes sense.

Hospital - Infections

Consider the following hypotheses:

H₀: μ = 470
H_A: μ ≠ 470

The population is normally distributed with a population standard deviation of 44. (You may find it useful to reference the appropriate table: z table or t table)

a-1. Calculate the value of the test statistic with x−x− = 483 and n = 65. (Round intermediate calculations to at least 4 decimal places and final answer to 2 decimal places.)
  
Test statistic = ?

a-2. What is the conclusion at the 10% significance level?
  

A) Do not reject H₀ since the p-value is greater than the significance level.

B) Do not reject H₀ since the p-value is less than the significance level.

C) Reject H₀ since the p-value is greater than the significance level.

D) Reject H₀ since the p-value is less than the significance level.

a-3. Interpret the results at αα = 0.10.

A) We cannot conclude that the population mean differs from 470.

B) We conclude that the population mean differs from 470.

C) We cannot conclude that the sample mean differs from 470.

D) We conclude that the sample mean differs from 470.

b-1. Calculate the value of the test statistic with x−x− = 438 and n = 65. (Negative value should be indicated by a minus sign. Round intermediate calculations to at least 4 decimal places and final answer to 2 decimal places.)
  
Test statistic = ?

b-2. What is the conclusion at the 5% significance level?
  

A) Reject H₀ since the p-value is greater than the significance level.

B) Reject H₀ since the p-value is less than the significance level.

C) Do not reject H₀ since the p-value is greater than the significance level.

D) Do not reject H₀ since the p-value is less than the significance level.

b-3. Interpret the results at αα = 0.05.

A) We conclude that the population mean differs from 470.

B) We cannot conclude that the population mean differs from 470.

C) We conclude that the sample mean differs from 470.

D) We cannot conclude that the sample mean differs from 470.

Suppose that the average number of Facebook friends users have is normally distributed with a mean of 117 and a standard deviation of about 45. Assume forty-seven individuals are randomly chosen. Answer the following questions. Round all answers to 4 decimal places where possible. What is the distribution of ¯ x x¯ ? ¯ x x¯ ~ N(,) For the group of 47, find the probability that the average number of friends is more than 121. Find the third quartile for the average number of Facebook friends. For part b), is the assumption that the distribution is normal necessary? NoYes

The production of wine is a​ multibillion-dollar worldwide industry. In an attempt to develop a model of wine quality as judged by wine​ experts, data was collected from red wine variants. A sample of 20 wines is provided in the accompanying table. Develop a multiple linear regression model to predict wine​ quality, measured on a scale from 0​ (very bad) to 10​ (excellent) based on alcohol content​ (%) and the amount of chlorides. Complete parts a through g below. LOADING... Click the icon to view the table. a. State the multiple regression equation. Let Upper X Subscript 1 i represent the alcohol content​ (%) of wine i and let Upper X Subscript 2 i represent the number of chlorides for wine i. Quality Alcohol_Content(%) Chlorides 0 7.9 0.067 1 7.1 0.062 2 8.9 0.067 2 8.1 0.071 2 8.6 0.073 3 8.9 0.074 2 9.3 0.072 5 9.5 0.077 6 10.4 0.077 7 10.3 0.079 7 10.1 0.083 6 10.9 0.084 7 11.4 0.081 7 11.4 0.084 6 11.9 0.095 9 11.5 0.096 8 11.7 0.119 9 11.5 0.143 10 12.3 0.151 9 12.3 0.159 b. Interpret the meaning of the​ slopes, b 1 and b 2​, in this problem. c. Explain why the regression​ coefficient, b 0​, has no practical meaning in the context of this problem. c. Predict the mean quality rating for wines that have 8​% alcohol content and chlorides of 0.10. d. Construct a​ 95% confidence interval estimate for the mean quality rating for wines that have 8​% alcohol and 0.10 chlorides. e. Construct a​ 95% confidence interval estimate for the mean quality rating for wines that have 8​% alcohol and 0.10 chloride Construct a​ 95% prediction interval estimate for the quality rating for an individual wine that has 8​% alcohol and 0.10 chlorides. h. What conclusions can you reach concerning this regression​ model?