A random sample of 42 textbooks has a mean price of $114.50 and a standard deviation of $12.30. Find a 98% confidence interval for the mean price of all textbooks. *

A researcher found that age (X) and annual income (Y) were correlated with r = 0.50. For age, M = 50 and SD = 10. For annual income (in thousands of dollars), M = 60 and SD = 10. The intercept of the regression line was found to be 35. What is the value of the slope of the regression line?

anova stats questions

1. If the treatment Sum of Squares is 400, and k=5, what is the treatment variance?

2. For three conditions with five scores in each condition, what is df_total?

3. What is the table value for F_(11,46) when alpha = .05?

4. What is the lowest possible value for the F statistic?

5. Given: F_(2,25). What is F_(crit) for alpha = .01?

6. Given: F_(5,25). What is k?

7. Given: F_(1,25). What is N?

A relief fund is set up to collect donations for the families affected by recent storms. A random sample of 400 people shows that 45 of those 200 who were contacted by telephone actually made contributions compared to only 35 of the 200 who received first class mail requests.

The 95% confidence interval for the difference in the proportions of people who make donations if contacted by telephone or first class mail is (round each answer to 4 places after the decimal):

lower end =

higher end =

Is there significant statistical evidence that the percent of people who were contacted by telephone and made a contribution is larger than the percent of people who received first class mail requests and made a contribution?

This interval contains all positive numbers, indicating that there is sufficient evidence to conclude that the percent of people who made a contribution after being contacted by telephone is greater than the percent of people who made a contribution after receiving first class mail requests.

This interval contains all negative numbers, indicating that there is sufficient evidence to conclude that the percent of people who made a contribution after receiving first class mail requests is greater than the percent of people who made a request after being contacted by telephone.  

  This interval contains zero, indicating that there is not sufficient evidence to conclude that the percent of people who made a contribution after being contacted by telephone is greater than the percent of people who made a contribution after receiving first class mail requests.

The owner of a new car dealership claims the average number of days it takes his dealership to sell a Chevrolet Aveo is 50 days. A random sample of 50 cars had a mean time on the dealer’s lot of 64 days. Assume the population standard deviation to be 7.0 days. Find the 95% confidence interval estimate of the population mean. State the Margin of Error, Best Point Estimate and Include the written statement

Please list all the work.

1. One tail or two tail test and why.

2. Null and alternative hypotheses.

3. Type of test and why.

4. Critical values at .05 and .01 levels. Include df, if needed.

5. Compute test

6. Accept or reject null (Remember to include level if reject.)

7. English conclusion (as we do in class).

16. People are selected to serve on juries by randomly picking names from the list of registered voters. The average age for registered voters in the country is μ = 39.6 years. A statistician randomly selects a sample of n = 16 people who are currently serving on juries. The average age for the sample is M = 48.9 years with a standard deviation = 12.4 years. Is the mean age of this sample significantly different than the mean age for registered voters? (18 points)

1. IV

      DV

2. Set up as a formal inferential proof.

3. Calculate the point estimate for the mean of the population.

Calculate the 99% confidence interval for the mean of the population

How to solve this question on Microsoft Excel

The annual commissions earned by sales representatives of Machine Products Inc., a manufacturer of light machinery, follow the normal distribution. The mean yearly amount earned is $40,000 and the standard deviation is $5000.

a. What percentage of sales representatives earn between $32,000 and $42,000 per year?

b. What percentage of sales representatives earn more than $42,000 per year?

c. The sales manager wants to award the sales representatives who earn the largest commissions a bonus of $1000. He can award a bonus to 20% of the representatives. What is the cutoff point between those who earn a bonus and those who do not?

A recent publication states that the average closing cost for purchasing a new home is $8586. A real estate agent believes the average closing cost is more than $8586. She selects 28 new home purchases and finds that the average closing costs are $8582 with a standard deviation of $341. Help her decide if she is correct by testing her claim at αα=0.01.

The correct hypotheses would be:

• H0:μ≤$8586H0:μ≤$8586
  HA:μ>$8586HA:μ>$8586 (claim)
• H0:μ≥$8586H0:μ≥$8586
  HA:μ<$8586HA:μ<$8586 (claim)
• H0:μ=$8586H0:μ=$8586
  HA:μ≠$8586HA:μ≠$8586 (claim)

Since the level of significance is 0.01 the critical value is 2.473

The test statistic is: (round to 3 places)

The p-value is: (round to 3 places)

The decision can be made to:

• reject H0H0
• do not reject H0H0

The final conclusion is that:

• There is enough evidence to reject the claim that the average closing cost is more than $8586.
• There is not enough evidence to reject the claim that the average closing cost is more than $8586.
• There is enough evidence to support the claim that the average closing cost is more than $8586.
• There is not enough evidence to support the claim that the average closing cost is more than $8586.

A new baker is trying to decide if he has an appropriate price set for his 3 tier wedding cakes which he sells for $84.68. He is particullarly interested in seeing if his wedding cakes sell for less than the average price. He searches online and finds 23 of the competitors in his area that sell 3 tier wedding cakes with a mean price of $87.73 with a standard deviation of $6.19. Help the new baker by testing his his claim with a 0.10 level of significance.

The correct hypotheses would be:

• H0:μ≤$84.68H0:μ≤$84.68
  HA:μ>$84.68HA:μ>$84.68 (claim)
• H0:μ≥$84.68H0:μ≥$84.68
  HA:μ<$84.68HA:μ<$84.68 (claim)
• H0:μ=$84.68H0:μ=$84.68
  HA:μ≠$84.68HA:μ≠$84.68 (claim)

Since the level of significance is 0.10 the critical value is 1.321

The test statistic is: (round to 3 places)

The p-value is: (round to 3 places)

The decision can be made to:

• reject H0H0
• do not reject H0H0

The final conclusion is that:

• There is enough evidence to reject the claim that his wedding cakes sell for less than the average price.
• There is not enough evidence to reject the claim that his wedding cakes sell for less than the average price.
• There is enough evidence to support the claim that his wedding cakes sell for less than the average price.
• There is not enough evidence to support the claim that his wedding cakes sell for less than the average price.

Students in the senior capstone course (N = 36) at University Uptight took the Political Science subtest developed by the National Bored Testing Association. The test is a 75-item, multiple-choice test covering all areas of political science. The national norms for the test show a mean of 50. The mean for the students in the capstone was 55, with a standard deviation of 15. Did the students at UU score significantly higher than the national norms?

A.State your null and alternative hypotheses.

B.Is this a one- or two-tailed hypothesis? Explain.

C.Calculate the appropriate statistical test.

D.Can you reject the null hypothesis? Why or why not?

E.What is the probability of a Type I error? Type II error?

F.Write a Results section for your findings. Include the descriptive statistics, type of statistical test and results of the test, and effect size.

G.Write a Discussion section for your findings. Include the findings, interpretation/explanation/implication of the findings, and possible next studies.

A researcher investigated the effects of green and red light on the growth rate of bean plants.  The table below summarizes the heights (in inches) of bean plants from soil to first branching stem.  

(A – 10 pts.)  Use the Pooled two-sample t-procedure to construct the 95% confidence interval for the difference in mean height for bean plants exposed to these two colors of light.  (You do not need to interpret the confidence interval.)

(B – 8 pts.)  Suppose that you wish to address the question of whether mean height differs for bean plants exposed to these two colors of light.  State the null hypothesis and the alternative hypothesis, using appropriate notation. Clearly identify what each symbol represents.  Do not attempt to conduct the test.

Beer and Diapers: There is a popular story (among data miners) that there is a correlation between men buying diapers and buying beer while shopping. A student tests this theory by surveying 160 male shoppers as they left a grocery store. The results are summarized in the contingency table below.

Observed Frequencies: O_i's

The Test: Test for a dependent relationship between buying beer and buying diapers. Conduct this test at the 0.01 significance level.

(a) What is the test statistic? Round your answer to 3 decimal places.

χ²

=

(b) What is the conclusion regarding the null hypothesis?

reject H₀fail to reject H₀    

(c) Choose the appropriate concluding statement.

The evidence suggests that all men who buy diapers also buy beer.The evidence suggests that the probability of a man buying beer is dependent upon whether or not he buys diapers.     There is not enough evidence to conclude that the probability of a man buying beer is dependent upon whether or not he buys diapers.We have proven that buying beer and buying diapers are independent variables.

Complete parts​ (a) through​ (h) for the data below.

x- 40, 50, 60, 70, 80

y-62, 58, 55, 47, 33

B) Find the equation of the line containing the points (50, 58) and (80, 33)

y=__x+(__)

D) By hand, determine the least-squares regression line

The equation of the​ least-squares regression line is given by

ModifyingAbove y with caret equals b 1 x plus b 0y=b1x+b0

where b1 equals r times StartFraction s Subscript y Over s Subscript x EndFractionb1=r•sysx

is the slope of the​ least-squares regression line and

b 0 equals y overbar minus b 1 x overbarb0=y−b1x

is the​ y-intercept of the​ least-squares regression line.

First find the correlation​ coefficient, r.

(f) Compute the sum of the squared residuals for the line found in part​ (b).

The residual is given by the formula below.

Residual=observed y−predicted y=y−y^

(g) Compute the sum of the squared residuals for the​ least-squares regression line found in part​(d).

The residual is given by the formula below.

Residual=observed y−predicted y=y−ModifyingAbove y with caret

Assume the population distribution is normally distributed, the weights (in 1000 grams) of a random sample of 10 boxes of cereal are:

10.2 10.1 10.1 9.7 10.3 9.8 9.9 9.8 10.4 10.3

(a) Find a 99% confidence interval for the mean weight of each box of cereal.

(b) Assume the population standard deviation is 30 grams. Construct a 96% confidence interval for the mean weight of each box of cereal.

(c) Assume the population standard deviation is given. If one decreases the sample size while keeping the same confidence level, what is the effect on the length of a confidence interval of a population mean? Justify your answer.

(d) Assume the population standard deviation is given. If one increases the confidence level while keeping the same sample size, what is the effect on the length of a confidence interval of a population mean? Justify your answer.

2. Let X be a uniform random variable over the interval (0, 1). Let Y = X(1-X). a. Derive the pdf for Y . b. Check the pdf you found in (a) is a pdf. c. Use the pdf you found in (a) to find the mean of Y . d. Compute the mean of Y by using the distribution for X. e. Use the pdf of Y to evaluate P(|x-1/2|<1/8). You cannot use the pdf for X. f. Use the pdf of X to evaluate P(|X-1/2|<1/8).