Consider two samples: one which has 3 observations with a mean of 8.3 and a standard deviation of 1.2, and another which has 10 observations with a mean of 3.0 and a standard deviation of 5.4. Based on these samples, what is likely to be true for the populations if we test at the 5% level?

• A. Only equal variances
• B. Only equal means
• C. Both equal means and equal variances
• D. Neither equal means nor equal variances

You are to play three games. In the first game, you draw a card, and you win if the card is a heart. In the second game, you toss two coins, and you win if one head and one tail are shown. In the third game, two dice are rolled and you win if the sum of the dice is 7 or 11. What is the probability that you win all three games? What is the probability that you win exactly two games?

Solve the question using Tree Diagram. Please give explanation for the answer.

Research Question:  What is the effect of gender on whether or not a student has a meal plan?

Using the variables Q7.1 (What is your gender?) and Q6.1 (Do you have a meal plan?) what is the appropriate test to determine whether gender has a significant effect on living situation (e.g., Chi-square, T Test, ANOVA, Correlation) and why (e.g., what type of variables are you analyzing)?

For spring 2013 senatorial election in Colorado between Democratic incumbent Allison Boxer and Republican challenger Carly Fiorina, the CNN exit poll of 3870 voters indicated that 2180 (56.3%) of those voters voted for Boxer and 1690 (43.7%) voted for Fiorina or another candidate.

Of the 9,534,523 Cali voters in the actual election, 54.7% voted for Boxer while 45.3% did not vote for Boxer (voted for Fiorina, other).

a) Identify the data distribution. Use 0 for Fiorina/other; 1 for Boxer.

b) Identify the population distribution: Use 0 for Fiorina/other; 1 for Boxer.

c) Find the population proportion, p and population standard deviation.

d) Demonstrate the sampling distribution of the sample proportion is approximately normally distributed.

e) Using your results, what is the sampling distribution of the sample proportion who voted for Barbara Boxer? You may use a descriptive to demonstrate.

1. Explain why, if “A” stands for “There is thunder” and “B” stands for “It is raining,” you would expect p(A|B) to be greater than P(A).
2. Suppose you have a fair coin which is equally likely to come up heads or tails. Let “A” stand for “the first toss comes up heads” and “B” stands for the 2^nd toss comes up heads.” Calculate the following:
3. P(A)=
4. P(B)=
5. P(A&B)=
6. P(B|A)=

Chapter 4, Section 3, Exercise 116 Lizards and Invasive Fire Ants This exercise addresses lizard behavior in response to fire ants. The red imported fire ant, Solenopsis invicta, is native to South America, but has an expansive invasive range, including much of the southern United States (invasion of this ant is predicted to go global). In the United States, these ants occupy similar habitats as fence lizards. The ants eat the lizards and the lizards eat the ants, and in either scenario the venom from the fire ant can be fatal to the lizard. A study explored the question of whether lizards learn to adapt their behavior if their environment has been invaded by fire ants. The researchers selected lizards from an uninvaded habitat (eastern Arkansas) and lizards from an invaded habitat (southern Alabama, which has been invaded for more than 70 years) and exposed them to fire ants. They measured how long it takes each lizard to flee and the number of twitches each lizard does. The data are stored in FireAnts. If lizards adapt their behavior to the fire ants, then lizards from the invaded habitats should flee from the fire ants faster than lizards from the uninvaded habitats. Test this hypothesis. Time to flee is measured in seconds, and lizards taking more than a minute to flee have recorded responses of 61 seconds. Let group 1 be lizards from invaded habitats and let group 2 be lizards from uninvaded habitats.

(b) Use StatKey or other technology to compute the p-value.

Round your answer to three decimal places.

p-value = ?

Dorothy Kelly sells life insurance for the Prudence Insurance Company. She sells insurance by making visits to her clients homes. Dorothy believes that the number of sales should depend, to some degree, on the number of visits made. For the past several years, she kept careful records of the number of visits (x) she made each week and the number of people (y) who bought insurance that week. For a random sample of 15 such weeks, the x and y values follow.

Σx = 248; Σy = 97; Σx² = 4,844; Σy² = 775; Σxy = 1,828

(a) Find x, y, b, and the equation of the least-squares line. (Round your answers for x and y to two decimal places. Round your least-squares estimates to three decimal places.)

(b) Draw a scatter diagram for the data. Plot the least-squares line on your scatter diagram.

(c) Find the sample correlation coefficient r and the coefficient of determination. (Round your answers to three decimal places.)

What percentage of variation in y is explained by the least-squares model? (Round your answer to one decimal place.)
%

(d) In a week during which Dorothy makes 21 visits, how many people do you predict will buy insurance from her? (Round your answer to one decimal place.)
people

One article describes a study of 81 randomly selected young adults with pierced tongues. The researchers found receding gums, which can lead to tooth loss, in 25 of the participants.

(a) Construct a 95% confidence interval for the proportion of young adults with pierced tongues who have receding gums. (Don’t forget to check all conditions necessary to your construction!)

(b) Write a sentence in which you correctly interpret the confidence interval you created.

(c) Would the interval you found in (a) have been wider, narrower, or the same width if only 60 young adults had been sampled?

(Please answer step-by-step. Typed work preferable.)

1. The following matrix displays the bivariate correlations between family size (X), weekly grocery bill (Y), and income (Z) for a random sample of 50 families.

a. First, list the values of the 3 unique correlations, identifying the two variables in each correlation in some way. (r_xy = ?; r_xz = ? r_yz = ?)

b. Which of the correlations is statistically significant at the .05 level? Be sure to record the information on which you base these conclusions. (This implies you will need to perform a hypothesis test assessing whether each correlation is large enough to suggest that a real association exists in the population from which the sample was drawn.)

Study Aim to determine the effect of four different types of tips in a hardness tester on the observed hardness of a metal alloy. Four Specimen of the alloy were obtained, and each tip was tested once on each specimen, producing the following data

a) Perform Anova using Minitab and present the table - please provide us with Minitab table?

b) is there an effect of the type of tips on the hardness.

c) Use fisher LSD to investigate the difference between the tips?

1. According to a labor union contract, the mean income for all senior-level assembly-line workers in a large company must be $520 per week. Women who work for the company think that men workers are being paid more than the standard set in the labor contract. A representative of a women’s group decides to test this claim about the mean income µ for men employees, using α = .05. In a random sample of nine men workers, she finds that the sample mean income is $610 per week and the sample standard deviation s is $90.

1. State the null and alternative hypotheses in symbols.

2. State the null and alternative hypotheses in words.

3. Is this a one-sided or a two-sided test? How do you know? (4 points)

4. Should you use a z-test or a t-test for this problem? Why?

5. Find the critical value of the test statistic.

6. Calculate the value of the test statistic for this sample.

7. Based on these results, can you reject the null hypothesis or not?

8. Write a sentence to explain your conclusion about the average weekly income of women workers compared to the labor contract’s standard of $520 per week.

Use the information to answer Q7-10 Clemson found that 6% students said that they were strongly opposed to increases in college tuition. Suppose we have a random sample of 200 students. Let ?̂be the sample proportion.

7. The mean of ?̂is ____.

8. The standard deviation (sometimes called standard error) of ?̂is ____. (4 decimal places)

9. Which of the following can best describe/explain the shape of ?̂?

A. We can’t determine the shape of ?̂.

B. ?̂follows normal distribution because: 1. The sample is random. 2. ? is large enough

C. ?̂follows normal distribution because: 1. The sample is random. 2. ? = 200 ≥ 30.

D. ?̂follows normal distribution because: 1. The sample is random. 2. ?? = 0.06(200) = 12 ≥ 5 and ?(1 − ?) = 0.94(200) = 188 ≥ 5.

10. What is the probability that more than 13 students out of this sample of size 200 are strongly opposed to increases in college tuition. (4 decimal places)

Suppose you gather data from 450 residents in Pullman, Washington about the number of crimes they think happen on a monthly basis in their neighborhood. The answers range from 0 (no crimes) to 50 (this person things 50 crimes happen in Pullman, WA per month). The mean response is 12.3 with a standard deviation of 4.4.

Using this information, construct a 90% confidence interval for the overall mean number of crimes the residents of Pullman think happen. Round all answers to 2 decimal points (0.00). Be sure to interpret your results.

7. Suppose that a particular brand of peanut butter is in fact favored by 47% of all moms. A consumer organization will take a random sample of 200 moms from across the country and will use ˆp, the sample proportion, to estimate p, the actual proportion of moms who favor that peanut butter brand.

(a) Is it reasonable to assume that the sampling distribution of ˆp is approximately normal? Justify.

(b) Compute the mean and standard deviation of the ˆp distribution. (Give your answer to four decimal places.)

(c) What is the approximate probability that the random sample will produce a ˆp value greater than .5, causing the consumer organization to incorrectly conclude that the majority of moms prefer this brand of peanut butter? (Give your answer to four decimal places.)