Rothamsted Experimental Station (England) has studied wheat production since 1852. Each year, many small plots of equal size but different soil/fertilizer conditions are planted with wheat. At the end of the growing season, the yield (in pounds) of the wheat on the plot is measured. For a random sample of years, one plot gave the following annual wheat production (in pounds).

3.81	4.11	3.96	4.26	3.78	3.79	4.09	4.42
3.89	3.87	4.12	3.09	4.86	2.90	5.01	3.39

Use a calculator to verify that, for this plot, the sample variance is s² ≈ 0.305.

Another random sample of years for a second plot gave the following annual wheat production (in pounds).

3.70	3.73	4.00	3.43	3.52	3.72	4.13	4.01
3.59	4.29	3.78	3.19	3.84	3.91	3.66	4.35

Use a calculator to verify that the sample variance for this plot is s² ≈ 0.095.

Test the claim that the population variance of annual wheat production for the first plot is larger than that for the second plot. Use a 1% level of significance.

(a) What is the level of significance?

State the null and alternate hypotheses.

H_o: σ₁² = σ₂²; H₁: σ₁² > σ₂²

H_o: σ₁² > σ₂²; H₁: σ₁² = σ₂²    

H_o: σ₂² = σ₁²; H₁: σ₂² > σ₁²

H_o: σ₁² = σ₂²; H₁: σ₁² ≠ σ₂²

(b) Find the value of the sample F statistic. (Use 2 decimal places.)

What are the degrees of freedom?

dfN
dfD

What assumptions are you making about the original distribution?

The populations follow dependent normal distributions. We have random samples from each population.

The populations follow independent normal distributions. We have random samples from each population.    

The populations follow independent normal distributions.

The populations follow independent chi-square distributions. We have random samples from each population.

(c) Find or estimate the P-value of the sample test statistic. (Use 4 decimal places.)

p-value > 0.100

0.050 < p-value < 0.100    

0.025 < p-value < 0.050

0.010 < p-value < 0.025

0.001 < p-value < 0.010

p-value < 0.001

(d) Based on your answers in parts (a) to (c), will you reject or fail to reject the null hypothesis?

At the α = 0.01 level, we reject the null hypothesis and conclude the data are not statistically significant.

At the α = 0.01 level, we reject the null hypothesis and conclude the data are statistically significant.    

At the α = 0.01 level, we fail to reject the null hypothesis and conclude the data are not statistically significant.

At the α = 0.01 level, we fail to reject the null hypothesis and conclude the data are statistically significant.

(e) Interpret your conclusion in the context of the application.

Fail to reject the null hypothesis, there is sufficient evidence that the variance in annual wheat production is greater in the first plot.

Reject the null hypothesis, there is insufficient evidence that the variance in annual wheat production is greater in the first plot.    

Reject the null hypothesis, there is sufficient evidence that the variance in annual wheat production is greater in the first plot.

Fail to reject the null hypothesis, there is insufficient evidence that the variance in annual wheat production is greater in the first plot.

Please be very clear in part b) show all steps please. I have trouble understanding that part. Thank you.

Whencoin1isflipped,itlandsonheadswithprob- ability .4; when coin 2 is flipped, it lands on heads with probability .7. One of these coins is randomly chosen and flipped 10 times.
(a) What is the probability that the coin lands on heads on exactly 7 of the 10 flips?
(b) Given that the first of these ten flips lands heads, what is the conditional probability that exactly 7 of the 10 flips land on heads?

A survey of 300 U.S. online shoppers was conducted. In response to the question of what would influence the shopper to spend more money online in 2012, 18% said free shipping, 13% said offering discounts while shopping, and 9% said product reviews. (Data extracted from “2012 Consumer Shopping Trends and Insights,” Steelhouse, Inc., 2012.)

a) Construct 95% confidence intervals of the population proportion of online shoppers who would be influenced to spend more money online in 2012 for “Free shipping”, “Discounts offered while shopping”, “Product reviews” respectively.

b) You have been asked to update the results of this study. Determine the sample size necessary to estimate the population proportions in part (a) within ±0.02, with 95% confidence.

Saeko owns a yarn shop and want to expands her color selection. Before she expands her colors, she wants to find out if her customers prefer one brand over another brand. Specifically, she is interested in three different types of bison yarn. She randomly selected 21 different days and recorded sales of each brand. 0.10 significance level, can she conclude that there is a difference in preference between brands?

	Misa's Bison	Yak-et-ty-Yaks	Buffalo Yarns
	799	776	799
	784	640	931
	807	822	794
	675	856	920
	795	616	731
	875	893	837
Total	4,735.00	4,603.00	5,012.00

What is the null hypothesis, alternative hyp, level of significance.

Use ANOVA single factor to find the F statistic

The following data represents a random sample of birth weignts (in kgs) of male babies born to mothers on a special vitamin supplement.

3.73
3.02
4.37
4.09
3.73
2.47
4.33
4.13
3.39
4.47
3.68
3.22
4.68
3.43

(a) Do the data follow a normal distribution?  ? Yes No
Report the P-value of the normality test:

(b) Do the data support the claim that the mean birth weight of male babies that have been subjected to the vitamin supplement is at least 3.39 kgs? Use the p-value approach, and regulate the probability of committing Type I error to 5%5% (α=0.05α=0.05).

The p-value is:

Use three decimals.
Does this support the claim  ? Yes No

An automotive parts supplier assesses the usability and quality of the door locks that they provide. The locks are manufactured at three different plants. The production manager wants to determine whether the plant affects the final product. The production manager collects data on locks from each plant, and gives a usability and quality rating. Data are found in the file Car Lock Ratings.

a) State the null and alternate hypothesis we would run to determine if the Usability rating across all three manufacturing plants is the same.

b) Run a one-way ANOVA on these data. Show output.

c) What conclusions can you make based on the p-value of this test?

d) Obtain boxplot, residuals scatter plot, and individual residual Normal probability plots.

e) Have all assumptions been met? Explain using your plots to illustrate your answer.

Usibility Rating
Plant A	Plant B	Plant C
5	6	5
6	4	4
5	5	6
6	4	6
6	3	5
5	4	7
4	5	6
3	5	5
4	6	4
5	5	4
4	5	4
3	6	5
6	7	5
7	7	6
8	6	5
6	7	6
8	6	6
7		5
6		6
5		7
6		5
7
7
8

in Pennsylvania Cash 5 lottery balls are numbered 1 to 43 right balls are selected does not replacement the order in which the balls are selected does not matter the term your probability of winning Pennsylvania Cash 5 with one ticket write your answers in fractions

An important application of regression analysis in accounting is in the estimation of cost. By collecting data on volume and cost and using the least squares method to develop an estimated regression equation relating volume and cost, an accountant can estimate the cost associated with a particular manufacturing volume. Consider the following sample of production volumes and total cost data for a manufacturing operation. Production Volume (units) Total Cost ($) 400 4,700 450 5,700 550 6,100 600 6,600 700 7,100 750 7,700 Compute b1 and b0 (to 1 decimal). b1 b0 Complete the estimated regression equation (to 1 decimal). = + x What is the variable cost per unit produced (to 1 decimal)? $ Compute the coefficient of determination (to 3 decimals). Note: report r2 between 0 and 1. r2 = What percentage of the variation in total cost can be explained by the production volume (to 1 decimal)? % The company's production schedule shows 500 units must be produced next month. What is the estimated total cost for this operation (to the nearest whole number)? $

The table t-value associated with 8 degrees of freedom and used to calculate a 99% confidence interval is _______.

Select one:

a. 3.355

b. 1.860

c. 1.397

d. 2.896

Cameron Sinclair, Information Services Manager with Global Financial Service (GFS), is studying employee use of GFS email for non-business communications. He plans to use a 95% confidence interval estimate of the proportion of email messages that are non-business; he will accept a 0.05 error. Previous studies indicate that approximately 30% of employee email is not business related. Cameron should sample _______ email messages.

Select one:

a. 14

b. 323

c. 457

d. 12

95% conf, n=41 , X bar=$67,600, s=18,484 use chi-square critical values Finding confidence interval for population standard deviation. Assume simple random sample has a normal distribution.

Health-Care Survey. In the spring of 2017, the Consumer Reports National Research Center conducted a survey of 1007 adults to learn about their major health-care con-cerns. The survey results showed that 574 of the respondents lack confidence they will be able to afford health insurance in the future.

a. What is the point estimate of the population proportion of adults who lack confidence they will be able to afford health insurance in the future.

b. At 90% confidence, what is the margin of error?

c. Develop a 90% confidence interval for the population proportion of adults who lack confidence they will be able to afford health insurance in the future.

d. Develop a 95% confidence interval for this population proportion

Explain Monte Carlo Sampling? Under what circumstances, can it be used? Elaborate on the application and limitations related to this sampling?

Given the follow data for two pooled samples, calculate %95 confidence interval for each

mean, 95% confidence interval for difference of means, and one-tailed p-value for the null hypothesis, “Y

not greater than X”.

a. sample X: n=12, mean = 20.0, std. deviation = 3.1

sample Y: n = 12, mean = 22.0, std. deviation = 3.1

b. Same as part a, except the mean of Y is 23.0

c. Same as part a, except the standard deviation of Y is 4.0

d. Same as part a, except sample size of Y is 20

a dentist wants to find out the average time taken by her hygienist for x rays and clean teeth for patients. she recorded the time to serve 24 randomly selected patients . construct a 99% confidence interval for the average time taken

Time
	36.80 39.80 38.60 38.30 35.80 32.60 38.70 34.50 37.00 32.00 40.90 33.80 37.10 31.00 35.10 38.20 36.60 38.80 39.60 39.70 35.10 38.20 32.70 40.50

Mean number of desks produced per week is 42 and population standard deviation is 4.67. the company has introduced new production methods. A random sample of 12 weeks production indicates 44 desks were produced each week. has the introduction of new production methods increased average number of desks produced each week at .05 significance level. Estimate the 95% confidence interval