We have been discussing inference in class for a while now. One of the aspects of the discussion is estimation using a confidence interval. Going into as much detail as you like, explain in your own words the purpose of confidence interval estimation. As part of the explanation, indicate what is being estimated, possibly using an example of some kind.

From a random sample of 100 male students at Hope College, 16 were left-handed. Using the theory-based inference applet, determine a 99% confidence interval for the proportion of all male students at Hope College that are left -handed.​ Round your answers to 4 decimal places, e.g. "0.7523.

1.) Explain why there is an inverse relationship between committing a Type I error and committing a Type II error. What is the best way to reduce both kinds of error?

2.) Define the sampling distribution of the mean

3.) A random sample of size 144 is taken from the local population of grade-school children. Each child estimates the number of hours per week spent watching TV. At this point, what can be said about the sampling distribution? (b) Assume that a standard deviation, σ, of 8 hours describes the TV estimates for the local population of schoolchildren. At this point, what can be said about the sampling distribution? (c) Assume that a mean, µ, of 21 hours describes the TV estimates for the local popula-tion of schoolchildren. Now what can be said about the sampling distribution? (d) Roughly speaking, the sample means in the sampling distribution should deviate, on average, about ___ hours from the mean of the sampling distribution and from the mean of the population. (e) About 95 percent of the sample means in this sampling distribution should be between ___ hours and ___ hours.

a) A researcher was interested in whether the female students who enrolled in her stats course were more interested in the topic than the males. The researcher obtained a random sample of 8 male and 8 female students and gathered their scores on an Interest in Statistical Topics (IST) Survey.

Girls’ IST scores: 21, 37, 22, 20, 22, 20, 22, 21

Boys’ IST scores: 20, 20, 20, 21, 21, 20, 23, 21

Test the researcher’s hypothesis using α =.05

1)A university financial aid office polled a random sample of 824 male undergraduate students and 731 female undergraduate students. Each of the students was asked whether or not they were employed during the previous summer. 568 of the male students and 391 of the female students said that they had worked during the previous summer. Give a 90% confidence interval for the difference between the proportions of male and female students who were employed during the summer.

Step 1 of 3:

Find the point estimate that should be used in constructing the confidence interval. Round your answer to three decimal places

Step 2 of 3:

Find the margin of error. Round your answer to six decimal places.

Step 3 of 3:

Construct the 90%confidence interval. Round your answers to three decimal places.

2)The water works commission needs to know the mean household usage of water by the residents of a small town in gallons per day. They would like the estimate to have a maximum error of 0.14 gallons. A previous study found that for an average family the standard deviation is 2.3 gallons and the mean is 15 gallons per day. If they are using a 99% level of confidence, how large of a sample is required to estimate the mean usage of water? Round your answer up to the next integer

3)Given two independent random samples with the following results:

n1        7          n2        11

x1bar   143      x2bar   162

s1        12        s2        33

data: n1=7 x‾1=143    s1=12   n2=11 x‾2=162 s2=33

Use this data to find the 90% confidence interval for the true difference between the population means. Assume that the population variances are equal and that the two populations are normally distributed.

Step 1 of 3:

Find the point estimate that should be used in constructing the confidence interval.

Step 2 of 3:

Find the margin of error to be used in constructing the confidence interval. Round your answer to six decimal places.

Step 3 of 3:

Construct the 90% confidence interval. Round your answers to the nearest whole number

Notice that scores for males have been consistently higher than scores for females. Why do you think this is the case? Do you think that changes in our education system could eliminate this gap? Defend your answer?

) Let X be the minimum of the two numbers obtained by rolling a die twice and Y the maximum.

a) Compute E(X).

b) Compute Var(X).

c) Compute E(Y).

Run a regression analysis on the following bivariate set of data with y as the response variable.

Find the correlation coefficient and report it accurate to three decimal places.
r =

What proportion of the variation in y can be explained by the variation in the values of x? Report answer as a percentage accurate to one decimal place. (If the answer is 0.84471, then it would be 84.5%...you would enter 84.5 without the percent symbol.)
r² = %

Based on the data, calculate the regression line (each value to three decimal places)

y =  x +

Predict what value (on average) for the response variable will be obtained from a value of 40.7 as the explanatory variable. Use a significance level of α=0.05α=0.05 to assess the strength of the linear correlation.

What is the predicted response value? (Report answer accurate to one decimal place.)
y =

6.1

16. ASSUME THAT A RANDOMLY SELECTED SUBJECT IS GIVEN A BONE DENSITY TEST. THOSE TEST SCORES ARE NORMALLY DISTRIBUTED WITH A MEAN OF 0 AND A STANDARD DEVIATION OF 1. FIND THE PROBABILITY THAT A GIVEN SCORE IS LESS THAN 1.66. THE PROBABILITY IS.......(ROUND TO 4 DECIMAL PLACES AS NEEDED)

17.ASSUME THAT A RANDOMLY SELECTED SUBJECT IS GIVEN A BONE DENSITY TEST. THOSE TEST SCORES ARE NORMALLY DISTRIBUTED WITH A MEAN OF 0 AND A STANDARD DEVIATION OF 1. FIND THE PROBABILITY OF A BONE DENSITY TEST SCORE GREATER THAN 0.66. THE PROBABILITY IS.......(ROUND TO 4 DECIMAL PLACES AS NEEDED)

18. ASSUME THAT A RANDOMLY SELECTED SUBJECT IS GIVEN A BONE DENSITY TEST. THOSE TEST SCORES ARE NORMALLY DISTRIBUTED WITH A MEAN OF 0 AND A STANDARD DEVIATION OF 1. FIND THE PROBABILITY OF A BONE DENSITY TEST SCORE GREATER THAN -1.98. THE PROBABILITY IS.......(ROUND TO 4 DECIMAL PLACES AS NEEDED)

19.ASSUME THAT A RANDOMLY SELECTED SUBJECT IS GIVEN A BONE DENSITY TEST. THOSE TEST SCORES ARE NORMALLY DISTRIBUTED WITH A MEAN OF 0 AND A STANDARD DEVIATION OF 1. FIND THE PROBABILITY OF A BONE DENSITY TEST SCORE BETWEEN -1.81 AND 1.81. THE PROBABILITY IS.......(ROUND TO 4 DECIMAL PLACES AS NEEDED)

In the state of New York, a sample of 25 pregnant mothers takes a vitamin supplement. For this sample, the mean birth weight of the babies is 7.9 pounds with a standard deviation of 1.45 pounds. Find the 95% confidence interval for m - the mean birth weight for all babies whose mothers take the supplement . State the lower, upper limits for the interval.

The manager of a computer software company wishes to study the number of hours senior executives by type of industry spend at their desktop computers. The manager selected a sample of five executives from each of three industries. At the .05 significance level, can she conclude there is a difference in the mean number of hours spent per week by industry?

A marketing organization wishes to study the effects of four sales methods on weekly sales of a product. The organization employs a randomized block design in which three salesman use each sales method. The results obtained are given in the following table, along with the Excel output of a randomized block ANOVA of these data.

(a) Test the null hypothesis H₀ that no differences exist between the effects of the sales methods (treatments) on mean weekly sales. Set α = .05. Can we conclude that the different sales methods have different effects on mean weekly sales?

F = 16.98, p-value = .0025; (Click to select)RejectDo not reject H₀: there is (Click to select)a differenceno difference in effects of the sales methods (treatments) on mean weekly sales.

(b) Test the null hypothesis H₀ that no differences exist between the effects of the salesmen (blocks) on mean weekly sales. Set α = .05. Can we conclude that the different salesmen have different effects on mean weekly sales?

F = 43.43, p-value = .0003; (Click to select)RejectDo not reject H₀: salesman (Click to select)dodo not have an effect on sales

(c) Use Tukey simultaneous 95 percent confidence intervals to make pairwise comparisons of the sales method effects on mean weekly sales. Which sales method(s) maximize mean weekly sales? (Round your answers to 2 decimal places. Negative amounts should be indicated by a minus sign.)

Provide at least one example of a parametric statistical test and its nonparametric equivalent, and explain how these examples illustrate the comparison of the two types of analysis

[Using SAS]

1. The data (TET) relates to a study by Reiter and others (1981) concerning the effects of injecting triethyl-tin (TET) into rats once at age 5 days. The animals were injected with 0, 3 or 6 mg per kilogram of body weight (three levels). The response was the log of the activity count for 1 hour, recorded as 21 days of age. The rat was left to move about freely in a figure 8 maze. In this question, we will choose LOGACT21 as our response, the factor DOSAGE will be considered. (You will choose significance level at .05).

a. One wants to investigate whether Dosage level will have any impact on LOGACT21. Please write out the appropriate linear model.

b. Test the hypothesis that Dosage level will have impact on LOGACT21. Set up the null and alternative hypotheses; Report the P-value and make your conclusion from SAS result.

2. Still on data TET. In this question, we will choose LOGACT21 as our response, the two factors DOSAGE and SEX will be considered. (You will choose significance level at .05).

a. Set up appropriate model for this data (including the possible interaction terms).

b. (Interaction effect) Test the hypothesis that the gender effect is the same for all three levels of DOSAGE. Set up appropriate model, hypotheses and report your results.

c. Considering the model without the interactions, does SEX have any significant impact on the mean value of LOGACT21? Set up appropriate model, hypotheses and report your results.

d. Considering the model without the interactions, does DOSAGE have any significant impact on the mean value of LOGACT21? Set up appropriate model, hypotheses and report your results.

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Data file contents:

ID   LOGACT21   Dosage   Sex
1   2.636   0   Male
2   2.736   0   Male
3   2.775   0   Male
4   2.672   0   Male
5   2.653   0   Male
6   2.569   0   Male
7   2.737   0   Male
8   2.588   0   Male
9   2.735   0   Male
10   2.444   3   Male
11   2.744   3   Male
12   2.207   3   Male
13   2.851   3   Male
14   2.533   3   Male
15   2.63   3   Male
16   2.688   3   Male
17   2.665   3   Male
18   2.517   3   Male
19   2.769   3   Male
20   2.694   6   Male
21   2.845   6   Male
22   2.865   6   Male
23   3.001   6   Male
24   3.043   6   Male
25   3.066   6   Male
26   2.747   6   Male
27   2.894   6   Male
28   1.851   6   Male
29   2.489   6   Male
30   2.494   0   Female
31   2.723   0   Female
32   2.841   0   Female
33   2.62   0   Female
34   2.682   0   Female
35   2.644   0   Female
36   2.684   0   Female
37   2.607   0   Female
38   2.591   0   Female
39   2.737   0   Female
40   2.22   3   Female
41   2.371   3   Female
42   2.679   3   Female
43   2.591   3   Female
44   2.942   3   Female
45   2.473   3   Female
46   2.814   3   Female
47   2.622   3   Female
48   2.73   3   Female
49   2.955   3   Female
50   2.54   6   Female
51   3.113   6   Female
52   2.468   6   Female
53   2.606   6   Female
54   2.764   6   Female
55   2.859   6   Female
56   2.763   6   Female
57   3   6   Female
58   3.111   6   Female
59   2.858   6   Female

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Can someone walk me through how to do this on SAS? The documentation doesn't have any examples that break things down simply (I've never used SAS before this class) and the professor has snippets of code without context of what part is doing what. This is what I have so far:

data file;
infile 'pathhere'
getnames=yes
delimiter='09'x;
proc print;
run;

I know he wants a multiple linear regression model but I really don't understand what is supposed to go where code wise for SAS.

Question one

The following table gives the distribution of marks of 60 students in applied statistics test

1. Calculate the:
2. Mean, mode, median and define statistics                     
3. Lower quartile , upper quarter, Interquartile range
4. A researcher has extracted two samples from the same target population, sample A and sample B. Sample A has a mean of 25 kg while sample B has a mean twice that of sample A. Sample size of sample A is three times more than that of sample B. Sum of sample sizes is 60. Calculate:

1. Mean of sample B (1mark)
2. Sample size of sample A and sample B
3. Summation of x variables for sample A and sample B
4. Standard deviation of sample A and sample B, consider ungrouped data