GRADED PROBLEM SET #8

Answer each of the following questions completely. When possible to answer using a complete sentence and offering explanation, please do so. There are a total of 20 points possible in the assignment.

1. Resveratrol, an ingredient in red wine and grapes, has been shown to promote weight loss in rodents. One study investigates whether the same phenomenon holds true in primates. The grey mouse lemur, a primate, demonstrates seasonal spontaneous obesity in preparation for winter, doubling its body mass. A sample of six lemurs had their resting metabolic rate, body mass gain, food intake, and locomotor activity measured for one week prior to resveratrol supplementation (to serve as a baseline) and then the four indicators were measured again after treatment with a resveratrol supplement for four weeks. Some p-values for tests comparing the mean differences in these variables are given below. In parts a-d, state the conclusion of the test using a 5% significance level, and interpret the conclusion in context. (HINT: For thinking of the null/alternative hypothesis, the null would be that there is no change and the alternative would be what they are trying to test as described in the wording in each part)
   1. In a test to see if mean resting metabolic rate is higher after treatment, p=0.013

2. In a test to see if mean body mass gain is lower after treatment, p=0.007

3. In a test to see if mean food intake is affected by the treatment, p=0.035

4. In a test to see if locomotor activity is affected by the treatment, p=0.980

5. In which test is the strongest evidence for rejecting the null found? The weakest?

6. How do your answers to parts a-d change if the researchers make their conclusions using a stricter 1% significance level?

2. There were 2430 Major League Baseball games played in 2009, and the home team won the game in 53% of the games. If we consider the games played in 2009 as a sample of all MLB games, test to see if there is evidence, at the 5% level, that the home team wins more than half the games. (Show all steps of the hypothesis test to receive points)

Case 1 Instruction (Accounting Application) Use the MS Excel tabular graphical methods of descriptive statistics to summarize the sample data in the data set named PelicanStores in Case 1 folder. The managerial report should contain summaries such as:

1. A frequency and relative frequency distributions for the methods of payment (different cards). (20%)

2. Mean, median, first quartile, third quartile, and sample standard deviation for net sales from regular customers. (20%)

3. Mean, median, first quartile, third quartile, and sample standard deviation for net sales from married female. (20%)

4. Apply the location method to calculate the 60th percentile manually of net sales for each method (card) of payment. Please indicate which card has the highest 60th percentile and show the process. (20%)

5. Apply Chebyshev’s Theorem to calculate the range (i.e. $ to $) of at least 75% of the net sales must fall within for the Proprietary Card payment. (20%) (Hint: What is the z-score for at least 75% of data range?)

We need to find the confidence interval for the SLEEP variable. To do this, we need to find the mean and standard deviation with the Week 1 spreadsheet. Then we can the Week 5 spreadsheet to find the confidence interval.

First, find the mean and standard deviation by copying the SLEEP variable and pasting it into the Week 1 spreadsheet. Write down the mean and the sample standard deviation as well as the count. Open the Week 5 spreadsheet and type in the values needed in the green cells at the top. The confidence interval is shown in the yellow cells as the lower limit and the upper limit.

1. Give and interpret the 95% confidence interval for the hours of sleep a student gets. Change the confidence level to 99% to find the 99% confidence interval for the SLEEP variable.

2. Give and interpret the 99% confidence interval for the hours of sleep a student gets.

3. Compare the 95% and 99% confidence intervals for the hours of sleep a student gets. Explain the difference between these intervals and why this difference occurs.

In the Week 2 Lab, you found the mean and the standard deviation for the HEIGHT variable for both males and females. Use those values for follow these directions to calculate the numbers again.

(From Week 2 Lab: Calculate descriptive statistics for the variable Height by Gender. Click on Insert and then Pivot Table. Click in the top box and select all the data (including labels) from Height through Gender. Also click on “new worksheet” and then OK. On the right of the new sheet, click on Height and Gender, making sure that Gender is in the Rows box and Height is in the Values box. Click on the down arrow next to Height in the Values box and select Value Field Settings. In the pop up box, click Average then OK. Write these down.

Then click on the down arrow next to Height in the Values box again and select Value Field Settings. In the pop up box, click on StdDev then OK. Write these values down.)

You will also need the number of males and the number of females in the dataset. You can either use the same pivot table created above by selecting Count in the Value Field Settings, or you can actually count in the dataset. Then use the Week 5 spreadsheet to calculate the following confidence intervals. The male confidence interval would be one calculation in the spreadsheet and the females would be a second calculation.

4. Give and interpret the 95% confidence intervals for males and females on the HEIGHT variable. Which is wider and why?

5. Give and interpret the 99% confidence intervals for males and females on the HEIGHT variable. Which is wider and why?

6. Find the mean and standard deviation of the DRIVE variable by copying that variable into the Week 1 spreadsheet. Use the Week 4 spreadsheet to determine the percentage of data points from that data set that we would expect to be less than 40. To find the actual percentage in the dataset, sort the DRIVE variable and count how many of the data points are less than 40 out of the total 35 data points. That is the actual percentage. How does this compare with your prediction? Mean ______________ Standard deviation ____________________ Predicted percentage ______________________________ Actual percentage _____________________________ Comparison ___________________________________________________ ______________________________________________________________

7. What percentage of data would you predict would be between 40 and 70 and what percentage would you predict would be more than 70 miles? Use the Week 4 spreadsheet again to find the percentage of the data set we expect to have values between 40 and 70 as well as for more than 70. Now determine the percentage of data points in the dataset that fall within this range, using same strategy as above for counting data points in the data set. How do each of these compare with your prediction and why is there a difference? Predicted percentage between 40 and 70 ______________________________ Actual percentage _____________________________________________ Predicted percentage more than 70 miles ________________________________ Actual percentage ___________________________________________ Comparison ____________________________________________________ _______________________________________________________________ Why? __________________________________________________________ ________________________________________________________________

Use the Central Limit Theorem to find the mean and standard error of the mean of the sampling distribution. Then sketch a graph of the sampling distribution. The mean price of photo printers on a website is ​$228 with a standard deviation of ​$61. Random samples of size 34 are drawn from this population and the mean of each sample is determined. What is the standard deviation of the distribution of sample means ? (Type an integer or decimal rounded to three decimal places as​ needed.)

A study of 800 homeowners in a certain area showed that the average value of the homes is $182,000 and the standard deviation is $15,000. Find the probability that the mean value of these homes is less than $185,000.

Round answer to 4 decimal places.

1) Using the tdist function, calculate exact p-values for a two tailed test for the following test statistics (6 points)

a) 2.14, df = 79 (2 points) b) 3.68, df = 13 (2 points) c) 1.78, df = 117 (2 points)

Based on data from a​ college, scores on a certain test are normally distributed with a mean of 1518 and a standard deviation of 324.

Standard score   Percent
-3.0   0.13
-2.5   0.62
-2   2.28
-1.5   6.68
-1   15.87
-0.9   18.41
-0.5   30.85
-0.1   46.02
0   50.00
0.10   53.98
0.5   69.15
0.9   81.59
1   84.13
1.5   93.32
2   97.72
2.5   99.38
3   99.87
3.5   99.98

Find the percentage of scores greater than

2166

Find the percentage of scores less than

1194

Find the percentage of scores between

870

and

1680.

4000 B.C   1850 B.C.   150 A.D.
131   129   128
138   134   138
125   136   138
129   137   139
132   137   141
135   130   142
132   136   136
134   138   145
140   134   137

The values in the table below are measured maximum breadths​ (in millimeters) of male skulls from different epochs. Changes in head shape over time suggest that interbreeding occurred with immigrant populations. Use a 0.05 significance level to test the claim that the different epochs all have the same mean.

Find the p value

A random sample of size n=500 yielded p̂ =0.08
a) Construct a 95% confidence interval for p.
b) Interpret the 95% confidence interval.
c) Explain what is meant by the phrase "95% confidence interval."

Please try to type your solution for this question, so I can read it without a problem. I truly appreciate you for typing in advance.

The Question:

For some Mechanical Engineer students, data for 224 student’s GPAs in their first 4 semesters of college were compared using several predictors, namely HSM, HSS, HSE, SATM, and SATV. Here significant level α is 0.05.

Then, the researcher fit a regression model and got the following results (intercept is included in the model):

ANOVA Table

Parameter Estimates Table

1. What are the values for (A), (B), (C), (D), (E), (F) and (G)?

2. State the multiple regression model for this problem.

3. What % of the variation in GPA are we explaining by the multiple regression?

4. Specify the prediction equation (Include all the regressors)

5. Determine if this is a significant model, i.e. check ANOVA table. (If significant, then p-value < α.) Here significant level α is 0.05.

6. Determine if each predictor variable is significant to the model, give the reason, based on the JMP output (i.e. compare the test statistics or p-value)

Describe the sampling distribution of ModifyingAbove p with caret. Assume the size of the population is 25 comma 000. nequals900​, pequals0.235 Describe the shape of the sampling distribution of ModifyingAbove p with caret. Choose the correct answer below. A. The shape of the sampling distribution of ModifyingAbove p with caret is not normal because n less than or equals 0.05 Upper N and np left parenthesis 1 minus p right parenthesis greater than or equals 10. B. The shape of the sampling distribution of ModifyingAbove p with caret is approximately normal because n less than or equals 0.05 Upper N and np left parenthesis 1 minus p right parenthesis greater than or equals 10. C. The shape of the sampling distribution of ModifyingAbove p with caret is approximately normal because n less than or equals 0.05 Upper N and np left parenthesis 1 minus p right parenthesis less than 10. D. The shape of the sampling distribution of ModifyingAbove p with caret is not normal because n less than or equals 0.05 Upper N and np left parenthesis 1 minus p right parenthesis less than 10. Determine the mean of the sampling distribution of ModifyingAbove p with caret. mu Subscript ModifyingAbove p with caret Baseline equals 0.235 0.235 ​(Round to three decimal places as​ needed.) Determine the standard deviation of the sampling distribution of ModifyingAbove p with caret. sigma Subscript ModifyingAbove p with caret Baseline equals nothing ​(Round to three decimal places as​ needed.)

this question, but calculate the 90% confidence interval for the coefficient for cable by hand (but use the SE from the software output) and do the test whether age and number of TVs should be dropped by hand (use ANVOA table to get p-value and confirm with software).

The data in the table below contains observations on age, sex (male = 0, female = 1), number of television sets in the household, cable (no = 0, yes = 1), and number of hours of television watched per week. Using hours of television watched per week as the response, you can use Minitab's Regress or R's lm() command [e.g., model <- lm(hours~age+sex+num.tv+cable)] to fit a least squares regression model to all the other given variables.

What is the estimated value of the regression coefficient for age?  [2 pt(s)]

What is the estimated value of the regression coefficient for cable?  [2 pt(s)]

According to the regression equation, which of the following statements is true?
Females watch television 3.577 hours more per week than males.
Males watch television 3.577 hours more per week than females.
From the data given, one can not tell which gender watches more television per week.
Females watch television approximately the same number of hours per week as males.
[2 pt(s)]

What is the value of the test-statistic for the overall regression significance test?  [3 pt(s)]

What are the degrees of freedom associated with the test-statistic? Numerator:  Denominator:  [1 pt(s)]

Select the interval below that contains the p-value for this test.
p-value ≤ 0.001
0.001 < p-value ≤ 0.01
0.01 < p-value ≤ 0.05
0.05 < p-value ≤ 0.1
0.1 < p-value ≤ 0.25
p-value > 0.25
[3 pt(s)]

Compute a 90% confidence interval for the coefficient for cable. Lower Bound:  Upper Bound:  [3 pt(s)]

Compute a 95% confidence interval for the mean number of hours watched by 18-year old females with cable and 2 TV sets. Lower Bound:  Upper Bound: [3 pt(s)]

Compute a 95% prediction interval for the mean number of hours watched by 18-year old females with cable and 2 TV sets. Lower Bound:  Upper Bound: [3 pt(s)]

Test whether age and number of TV sets are needed in the model or should be dropped. What is the value of the test-statistic?  [3 pt(s)]

What are the degrees of freedom associated with this test? Numerator:  Denominator:  [1 pt(s)]

Select the interval below that contains the p-value for this test.
p-value ≤ 0.001
0.001 < p-value ≤ 0.01
0.01 < p-value ≤ 0.05
0.05 < p-value ≤ 0.1
0.1 < p-value ≤ 0.25
p-value > 0.25
[3 pt(s)]

You are conducting a multinomial Goodness of Fit hypothesis test for the claim that the 4 categories occur with the following frequencies:

H o : p A = 0.15 ; p B = 0.4 ; p C = 0.3 ; p D = 0.15 Complete the table.

Report all answers accurate to three decimal places.

1)

2) What is the chi-square test-statistic for this data?

χ 2 =

Significance level alpha is 0.005.

3) What is the p-value?

p-value =

4) What would be the conclusion of this hypothesis test?

A)Reject the Null Hypothesis

B)Fail to reject the Null Hypothesis

Report all answers accurate to three decimal places.