When circuit boards used in the manufacture of compact disc players are tested, the long run percentage of defectives is 5%. suppose that a batch of 250 boards has been received and that the condition of any particular board is independent of that of any other board.

a) Calculate the exact probability that at least 10 of the boards in the batch are defective

b) Calculate the approx probability that at least 10 of the boards in the batch are defective using a normal distribution

(Please do these problems using a R software) this is a computer assignment (show work)

Data from a one-way layout are given below. Four treatments correspond to area sizes 0.016, 0.030, 0.044 and 0.058. You may regard them simply as treatments A, B, C and D.

(a) Construct the ANOVA table (follow lecture example to get all relevant quantities computed. Use a single line R-command only for verification).

(b) Use F-test for no difference in their means. State your statistical conclusion in a full sentence (e.g. the treatments are found statistically significantly different at 5% level).

(c) Carry out multiple comparisons for treatment differences (construct 95% simultaneous confidence intervals by the Tukey’s method).

data:

area velocity

0.016 294.9

0.016 294.1

0.016 301.7

0.016 307.9

0.016 285.5

0.016 298.6

0.016 303.1

0.016 305.3

0.016 264.9

0.016 262.9

0.016 256

0.016 255.3

0.016 256.3

0.016 258.2

0.016 243.6

0.016 250.1

0.03 295

0.03 301.1

0.03 293.1

0.03 300.6

0.03 285

0.03 289.1

0.03 277.8

0.03 266.4

0.03 248.1

0.03 255.7

0.03 245.7

0.03 251

0.03 254.9

0.03 254.5

0.03 246.3

0.03 246.9

0.044 270.5

0.044 263.2

0.044 278.6

0.044 267.9

0.044 269.6

0.044 269.1

0.044 262.2

0.044 263.2

0.044 224.2

0.044 227.9

0.044 217.7

0.044 219.6

0.044 228.5

0.044 230.9

0.044 227.6

0.044 228.6

0.058 258.6

0.058 255.9

0.058 257.1

0.058 263.6

0.058 262.6

0.058 260.3

0.058 305.3

0.058 304.9

0.058 216

0.058 216

0.058 210.6

0.058 207.4

0.058 214.6

0.058 214.3

0.058 222.1

0.058 222.2

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