One factor in rating a National Hockey League team is the mean weight of its players. A random sample of players from the Detroit Red Wings was obtained. The weight (in pounds) of each player was carefully measured, and the resulting data have a sample size of 16 with a sample mean of 202 pounds and a sample standard deviation of 11.6 pounds. Assume that the distribution of the weights is normal. Please use 4 decimal places for all critical values.
(0.5 pts.) a) Find the 95% confidence interval for the true mean weight of the players from the Detroit Red Wings.
(0.5 pts.) b) Calculate the 95% lower bound of the true mean weight of the players from the Detroit Red Wings.
(1 pt.) Interpret your answer above (part b).
(1 pt.) c) Why is the lower limit from part a) different from the lower bound in part b)? Please explain your answer by listing the symbols that are different between parts a) and b) and explain why the symbols are used.
d) The 95% confidence interval of the weights for the Boston Bruins is (194.19, 205.81). If the true mean weights for the two teams are different, then it is likely that there will be a more physical game when the two teams meet. Is there any evidence to suggest that the true mean player weight of Detroit is different from that of Boston? Please explain your answer.
In: Math
What is a random number? and what are the criteria for a random number? For a research need that requires random numbers, a random number generator is needed, how does this random number generator work?
In: Math
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. In an effort to determine if rats perform certain tasks more quickly if offered larger rewards, the following experiment was performed. On day 1, a group of four rats was given a reward of one food pellet each time they climbed a ladder. A second group of four rats was given a reward of five food pellets each time they climbed a ladder. On day 2, the groups were reversed, so the first group now got five food pellets for each climb and the second group got only one pellet for climbing the same ladder. The average times in seconds for each rat to climb the ladder 30 times are shown in the following table. Rat A B C D E F G H Time 1 pellet 12.3 13.5 11.4 12.1 11.0 10.4 14.6 12.3 Time 5 pellets 11.1 12.4 12.2 10.6 11.5 10.5 12.9 11.0 Do these data indicate that rats receiving larger rewards tend to climb the ladder in less time? Use a 5% level of significance. (Let d = Time 1 − Time 5.) (a) What is the level of significance? State the null and alternate hypotheses. Will you use a left-tailed, right-tailed, or two-tailed test? H0: μd = 0; H1: μd < 0; left-tailed H0: μd = 0; H1: μd > 0; right-tailed H0: μd = 0; H1: μd ≠ 0; two-tailed H0: μd < 0; H1: μd = 0; left-tailed (b) What sampling distribution will you use? What assumptions are you making? The standard normal. We assume that d has an approximately uniform distribution. The standard normal. We assume that d has an approximately normal distribution. The Student's t. We assume that d has an approximately normal distribution. The Student's t. We assume that d has an approximately uniform distribution. What is the value of the sample test statistic? (Round your answer to three decimal places.) (c) Find (or estimate) the P-value. P-value > 0.250 0.125 < P-value < 0.250 0.050 < P-value < 0.125 0.025 < P-value < 0.050 0.005 < P-value < 0.025 P-value < 0.005 Sketch the sampling distribution and show the area corresponding to the P-value. Maple Generated Plot Maple Generated Plot Maple Generated Plot Maple Generated Plot (d) Based on your answers in parts (a) to (c), will you reject or fail to reject the null hypothesis? Are the data statistically significant at level α? At the α = 0.05 level, we fail to reject the null hypothesis and conclude the data are statistically significant. At the α = 0.05 level, we reject the null hypothesis and conclude the data are statistically significant. At the α = 0.05 level, we fail to reject the null hypothesis and conclude the data are not statistically significant. At the α = 0.05 level, we reject the null hypothesis and conclude the data are not statistically significant. (e) State your conclusion in the context of the application. Fail to reject the null hypothesis, there is insufficient evidence to claim that the mean time for rats receiving larger rewards to climb the ladder is less. Reject the null hypothesis, there is insufficient evidence to claim that the mean time for rats receiving larger rewards to climb the ladder is less. Reject the null hypothesis, there is sufficient evidence to claim that the mean time for rats receiving larger rewards to climb the ladder is less. Fail to reject the null hypothesis, there is sufficient evidence to claim that the mean time for rats receiving larger rewards to climb the ladder is less.
In: Math
The amount of time (in minutes) that a party hat to wait to be seated in a restaurant has an exponential distribution with a mean 15. Find the probability that it will take between 10 and 20 minutes to be seated for a table. If a party has already waited 10 minutes for a table, what is the probability it will be at least another 5 minutes before they are seated? If the restaurant decides to give a free drink to the top 10% of customers who have to wait the longest, at least how long will a party have to wait in order to get a free drink?
In: Math
The data below are yields for two different types of corn seed that were used on adjacent plots of land. Assume that the data are simple random samples and that the differences have a distribution that is approximately normal. Construct a 95% confidence interval estimate of the difference between type 1 and type 2 yields. What does the confidence interval suggest about farmer Joe's claim that type 1 seed is better than type 2 seed? Type 1, 2098 1931 2053 2415 2207 2004 2221 1592 Type 2, 2065 1962 2061 2448 2145 1969 2146 1491 In this example, mu d is the mean value of the differences d for the population of all pairs of data, where each individual difference d is defined as the type 1 seed yield minus the type 2 seed yield. The 95% confidence interval is nothingless thanmu Subscript dless than nothing. (Round to two decimal places as needed.)
In: Math
Which are paired designs and which are two independent random sample designs? For each #, it's one or the other...
#1 (a) Study of shopping at Wal-Mart. Study is on whether more go in non-grocery door than the grocery door? Study is done by counting the number of people entering each door from 7-9pm every Monday for 2 months.
(b) Study of shopping at Wal-Mart, but to collect data the number of people entering each door from 7-9pm on non-grocery and grocery at random and NOT collect both each time together. For example, do a non-grocery count this Monday from 7-9pm, then non-grocery again Tuesday from 7-9pm, and then grocery on Wednesday from 7-9pm, etc.
#2 (a) Study is on the effect of magnetic fields on healing times. To collect data you take 100 random individuals prick a single finger on each. Half of them you use magnetic field on and the others you don't. You record healing time.
(b) Study is on the effect of magnetic fields on healing times. On each of the 100 participants you prick one finger on each hand. Apply magnetic field to one finger and nothing to the other. You measure healing times for fingers.
#3 (a) Taste testing is done in which each participant tries coke and pepsi both and rates them both. (b) Taste testing is done in which each person just tastes one and rates it and some other random person tastes the other and rates it.
#4 (a) Study of whether more movies are rented at Redbox on Friday or Saturday nights. Record rental numbers every week for 6 months on each Friday and the Saturday right after it.
(b) Study of whether more movies are rented at Redbox on Friday or Saturday. To get the data you randomly pick 24 Friday’s and then randomly pick 24 Saturday’s and record rentals on each. Note, it is NOT necessary for them to one right after the other.
#5 (a) Randomly pick 50 items that have been produced and use method one on it, then randomly pick another 50 and use method two on it.
(b) Match two items up because they came off production line together. Apply method one to one of them and method two to the other.
In: Math
1) What is the sum ∑ X Y?
2) What is the Pearson correlation coefficient (r) for the data below?
3)If you were to test the Pearson correlation coefficient for significance, what would be the critical value of t (alpha=.05)?
4) If you were to test the Pearson correlation coefficient for significance, what would be the computed value of t (alpha=.05)?
5)If you were to test the Pearson correlation coefficient for significance, what would be your conclusion (alpha=.05)?
6) For the data below, what is the value of "b" for the regression equation?
7)For the data below, what is the value of "a" for the regression equation?
8)For the data below, what is the IQ of the son if the father has an IQ of 100?
9)For the data below, what is the IQ of the son if the father has an IQ of 90?
10) For the data below, what is the IQ of the son if the father has an IQ of 80
11) For the data below, what is the standard error of the estimate for the previous predictions
| Family | Father | Son |
| 120 | 121 | |
| 110 | 105 | |
| 120 | 125 | |
| 92 | 87 | |
| 85 | 92 | |
| 72 | 90 | |
| 107 | 110 | |
| 115 | 122 | |
| 155 | 133 | |
| 90 | 123 |
In: Math
The birth weights for two groups of babies were compared in a study. In one group the mothers took a zinc supplement during pregnancy. In another group, the mothers took a placebo. A sample of 98 babies in the zinc group had a mean birth weight of 3423 grams. A sample of 80 babies in the placebo group had a mean birth weight of 3004 grams. Assume that the population standard deviation for the zinc group is 686 grams, while the population standard deviation for the placebo group is 783 grams. Determine the 98% confidence interval for the true difference between the mean birth weights for "zinc" babies versus "placebo" babies.
Step 1 of 2:
Find the critical value that should be used in constructing the confidence interval.
Step 2 of 2:
Construct the 98%confidence interval. Round your answers to the nearest whole number.
In: Math
Statistics Problem:
You have been asked to engage in one final project for the political organization for which you have been working. This time you wish to study the nature of the relationship between the ages of the donors to the campaign and the amount of money they plan to donate or have donated. Data is collected from a random sample of supporters of the candidate. This data is shown on the next page. Various questions need to be answered about the results you generate. These questions follow the presentation of the data. You should answer the questions posed in the narrative that should accompany your results.
Data:
Age of Supporter Donation
22 $ 75
38 135
50 100
46 50
60 200
28 0
25 10
69 35
75 75
28 100
55 250
37 100
36 100
43 125
35 0
19 0
48 50
70 25
31 115
30 105
Questions:
l) Find a 95% confidence interval for the slope of the population regression line. Provide an explanation of the meaning of this interval. Show how this interval can be used in order to answer the question posed (at the 5% level of significance) in the previous part of the problem.
m) Find a 95% confidence interval for the mean donation for supporters of the candidate who are 30 years of age. Provide an explanation of the meaning of this interval.
n) Suppose a 95% confidence interval for the mean donation for supporters of the candidate who is 50 years of age is desired. Find this interval, explain its meaning, and compare its width to that of the interval computed in the previous part of the problem. Give a reason for any difference in the width between this interval and the one in the previous part of the problem.
o) Find a 95% prediction interval for the donation of an individual supporter of the candidate who is 30 years of age. Explain its meaning relative to the problem. Compare the width of this interval to that of the interval calculated in part m) of the problem. Give a reason for any difference in the width of this interval and the one you found in part m) earlier.
In: Math
two fair dice are each rolled once. Let X denote the absolute value of the difference between the two numbers that appear.
List all possible values of X
Find the probability distribution of X.
Find the probabilities P(2<X<5) and P(2£X<5).
Find the expected value mand standard deviation of X.
In: Math
THIS IS A DECISION ANALYSIS MAKING CLASS (HEALTHCARE ADMINISTRATION)
Discuss why probability is so important within the health care decision analysis. Provide specific areas of understanding, for Classical, Empirical, Subjective and Axiomatic Probability. Why are these Probability used in the health care decision analysis?
In: Math
Statistics Problem:
You have been asked to engage in one final project for the political organization for which you have been working. This time you wish to study the nature of the relationship between the ages of the donors to the campaign and the amount of money they plan to donate or have donated. Data is collected from a random sample of supporters of the candidate. This data is shown on the next page. Various questions need to be answered about the results you generate. These questions follow the presentation of the data. You should answer the questions posed in the narrative that should accompany your results.
Data:
Age of Supporter Donation
22 $ 75
38 135
50 100
46 50
60 200
28 0
25 10
69 35
75 75
28 100
55 250
37 100
36 100
43 125
35 0
19 0
48 50
70 25
31 115
30 105
Questions:
l) Find a 95% confidence interval for the slope of the population regression line. Provide an explanation of the meaning of this interval. Show how this interval can be used in order to answer the question posed (at the 5% level of significance) in the previous part of the problem.
m) Find a 95% confidence interval for the mean donation for supporters of the candidate who are 30 years of age. Provide an explanation of the meaning of this interval.
n) Suppose a 95% confidence interval for the mean donation for supporters of the candidate who is 50 years of age is desired. Find this interval, explain its meaning, and compare its width to that of the interval computed in the previous part of the problem. Give a reason for any difference in the width between this interval and the one in the previous part of the problem.
o) Find a 95% prediction interval for the donation of an individual supporter of the candidate who is 30 years of age. Explain its meaning relative to the problem. Compare the width of this interval to that of the interval calculated in part m) of the problem. Give a reason for any difference in the width of this interval and the one you found in part m) earlier.
In: Math
A poll printed the results of a survey of 880Americans focusing on their perception of the quality of Japanese products. It has been observed that the sentiment towards Japanese products has actually improved over time. Is there sufficient evidence to conclude that American sentiment towards Japanese products changed from 1999 to 2005?
| Opinion | 1999 | 2005 |
|---|---|---|
| Good to Excellent | 24% | 28% |
| Average | 27% | 40% |
| Below Average | 18% | 3% |
| No Opinion | 31% | 29% |
Step 1 of 10: State the null and alternative hypothesis.
Step 2 of 10: What does the null hypothesis indicate about the proportions of Americans in each rating category?
The proportions of Americans in each rating category are all thought to be equal.
or
The proportions of Americans in each rating category are different for each category (and equal to the previously accepted values).
Step 3 of 10: State the null and alternative hypothesis in terms of the expected proportions for each category.
Step 4 of 10: Find the expected value for the number of Americans who rate Japanese products good to excellent. Round your answer to two decimal places.
Step 5 of 10: Find the expected value for the number of Americans who rate Japanese products average. Round your answer to two decimal places.
Step 6 of 10: Find the value of the test statistic. Round your answer to three decimal places.
Step 7 of 10: Find the degrees of freedom associated with the test statistic for this problem.
Step 8 of 10: Find the critical value of the test at the 0.025 level of significance. Round your answer to three decimal places.
Step 9 of 10: Make the decision to reject or fail to reject the null hypothesis at the 0.025 level of significance.
Step 10 of 10: State the conclusion of the hypothesis test at the 0.025 level of significance.
In: Math
There are 2 data sets below, choose which statistic to use and
conduct your analysis . This is
completely up to you but note that your data will dictate what test
you will run (see the book for examples and then compare to the
examples below). Be creative and thorough in your analysis. I will
expect 2 write-ups for both data sets.
Note: You will again need to use the tables in the back of the book to determine significance. Which table will be determined by which statistic you choose to use.
Project A: Assess the differences between Southerners and Non-Southerners on Church Attendance per Month. Below are number of days per month attended by South and non-South residents.
South
NonSouth
16
8
13
5
12
4
15
8
11
1
Project B: Assess attitudes toward same-sex
marriages of non-politician republicans and democrats
Note: 0=disagree with same-sex marriages and 10 = Agree with
same-sex marriages
Republicans Democrats Independent
6
8 6
5
6
7
3
9 5
7
8
6
4
7
5
In: Math
5. Many cell phone service providers offer family plans wherein parents who subscribe can get discounts for other family members. Suppose that the number of cell phones per family is Poisson distributed with a mean of 1.5. If one family is randomly selected, calculate the following probabilities
a) Family has only 1 cell phone.
b) Family has 3 or more cell phones.
c) Family has 4 or fewer cell phones.
In: Math