​a) What is the confidence​ interval?

​(___ ​,____​)

Given the following data, find the percentile of a diameter of 1.40 inches. Diameters of Golf Balls (in Inches) 1.31 1.63 1.58 1.44 1.35 1.48 1.47 1.58 1.61 1.55 1.57 1.66 1.53 1.38 1.38 1.59 1.31 1.42 1.32 1.37

Allegiant Airlines charges a mean base fare of $84. In addition, the airline charges for making a reservation on its website, checking bags, and inflight beverages. These additional charges average $34 per passenger. Suppose a random sample of 50 passengers is taken to determine the total cost of their flight on Allegiant Airlines. The population standard deviation of total flight cost is known to be $40. Use z-table.

a. What is the population mean cost per flight?
$

b. What is the probability the sample mean will be within $10 of the population mean cost per flight (to 4 decimals)?

c. What is the probability the sample mean will be within $5 of the population mean cost per flight (to 4 decimals)?

The article entitled “Effect of metformin therapy on 2-h post-glucose insulin levels in patients of polycystic ovarian syndrome” by Saxena et al. discussed the influence of metformin on insulin levels in women with polycystic ovarian syndrome (POCS), http://www.ncbi.nlm.nih.gov/pmc/articles/PMC3017330/?tool=pubmed (Links to an external site.).
Summarize the article in terms of the statistics that were used and calculate the following statistics for i) the body mass index, ii) the FSH levels, and iii) the mean hirsutism scores (15 points):

a. The 95% and 99% confidence intervals.

b. Test the null and alternative hypothesis that the after treatment results are significantly different from the before treatment results.

Sample size=40

Exhibit 6-10a. You are asked to bid on a first edition copy of Snedecor's Statistical Methods at an auction. You are bidding for a friend and the friend gives you $11600 and tells you that if you win the item for her then you can keep whatever is left over and if you lose the auction then you simply return the $11600 to her. At the auction there is only one other bidder and you believe their bid for the item will be uniformly distributed between $2300 and $10100. The winner of the auction is the highest bidder and they pay the amount of the loser's bid (similar to eBay).

[R] Refer to Exhibit 6-10a. If you submit a bid of $8140 what is your expected profit, E(profit)? Note: profit is revenue minus cost.

Data has been gathered to explain executive salaries from a variety of factors.

Perform a Multiple Regression to predict SALARY from EXPerience, EDUCation, GENDER, NUMberSupported and ASSETS.

d. Test for violation of the Model Assumptions. How did you do this?

e. Test for multicollinearity. How did you do this?

A researcher wants to estimate the difference in the means of two populations. A random sample of 36 items from the first population results in a sample mean of 430. A random sample of 49 items from the second population results in a sample mean of 460. The population standard deviations are 120 for the first population and 140 for the second population. From this information, a 95% confidence interval for the difference between means of the first population and the second population is _______. Select one: a. -102.83 to 42.43 b. -87.60 to 27.60 c. -76.53 to 16.53 d. -95.90 to 35.90

A normally distributed population of lemming body weights has a mean of 63.5 g and a standard deviation of 12.2 g.

1. What proportion of this population is 43.0g or smaller?

2. If there are 1000 weights in the population, how many of them are 43.0 or smaller?

3. What is the probability of a body weight between 50.0 and 60.0 g?

An ogre is very hungry but cannot decide how many chickens he wants to eat. So, he rolls a standard 6-sided die. Let Y be the number that he rolls. Then he goes to his chicken coop and randomly chooses Y chickens to eat. Suppose that his coop has 10 Rhode Island Reds and 4 Bantams.

(a) What is the probability that all of the Bantams get eaten? (b) What is the expected number of Bantams consumed?

Researchers at Consumer Reports recently found that fish are often mislabeled in grocery stores and restaurants. They are interested to know, however, if the proportion of mislabeling varies by type of fish. They collected data on 400 packages of tuna and 300 packages of mahi mahi and found that 110 and 95 were mislabeled, respectively.

a. What are the point estimates for the proportion of tuna and mahi mahi that are mislabeled?

b. Provide a 95% confidence interval estimate of the difference between the proportion of tuna and mahi mahi that is mislabeled.

c. Based on your answer to (b), would you say the rate of mislabeling is different for tuna and mahi mahi? Explain your answer.

d. Now, let's say we want to test whether the proportion of tuna mislabeled is lower than the proportion of mislabeled mahi mahi. Assuming a 99% confidence level, work through your hypothesis testing procedure below.

Imagine a basketball player named Shack. He is getting old, doesn’t run too well and has always been a poor free-throw shooter. He decides to work on the last of these as follows:Five times per day for the next 80 days he will shoot four free throws and count thenumber of successes that he achieves.Thus, Shack will collect n = 400 numerical values, with each value being one of: 0, 1, 2, 3 or 4.Shack wants to use the Goodness of Fit Test to test whether these 400 values behave as if they come from a binomial distribution. Note p is unknown.His O’s are below.Outcome01234Oi251181399325(1)State the null hypothesis and alternative hypothesis. (2)Estimateπ.(3)Fill the following table and carry out a multinomial 2test with =0.05 BY HAND. Remember to state your conclusions.

Outcome 0 1 2 3 4

Oi 25 118 139 93 25

Pi

Ei

Oi-Ei

(Oi-Ei)2

(Oi-Ei)2/Ei

A simple random sample with n=56 provided a sample mean of 22.5 and a sample standard deviation of 4.4

a.Develop a 90% confidence interval for the populationmean.

b.Develop a 95% confidence interval for the populationmean.

c.Develop a 99% confidence interval for the populationmean.

d.What happens to the margin of error and the confidenceinterval as the confidence level is increased?

Below are sets of three variables. On the lines after each set, do the following: Write a hypotheses relating the first two variables. Identify independent and dependent variables. State how you expect the third variable to affect the hypothesized relationship. Draw an arrow diagram including all three variables. Determine whether the third variable is antecedent, intervening, or alternative. Primary caregiver for children (primary caregiver, not primary caregiver); support for Family Medical Leave Law (thermometer scale for support); gender (female, male) Intention to vote in upcoming election; respondent’s general interest in politics; predicted outcome of election (“too close to call,” “somewhat competitive,” “lopsided victory”) Type of lightbulb purchased (regular, energy efficient); difference in cost of regular and high-efficiency lightbulbs (small difference, large difference); concern about global climate change. The only answer given is that there aren't three variables. I really need help with this question.

To better understand how husbands and wives feel about their finances, a magazine conducted a national poll of 1,006 married adults age 25 and older with household incomes of $50,000 or more. Consider the following example set of responses to the question "Who is better at getting deals?"

(a)

Develop a joint probability table and use it to answer the following questions. (Round your answers to four decimal places.)

(b)

According to the marginal probabilities, what is the most likely response?

I ammy spouse    we are equal

(c)

Given that the respondent is a husband, what is the probability that he feels he is better at getting deals than his wife? (Round your answer to four decimal places.)

(d)

Given that the respondent is a wife, what is the probability that she feels she is better at getting deals than her husband? (Round your answer to four decimal places.)

(e)

Given a response "My spouse" is better at getting deals, what is the probability that the response came from a husband? (Round your answer to four decimal places.)

(f)

Given a response "We are equal," what is the probability that the response came from a husband?

What is the probability that the response came from a wife?

True or False The critical value is the number of standard errors on either side of the sample proportion.

True or False The margin of error is smaller for a 95% confidence interval than for a 90% confidence interval.

True or False Type II Error is caused by rejecting the null hypothesis when the null hypothesis was actually true.

True or False Type I and Type II errors are related. The only way to decrease both is to decrease the sample size.

True or False A small P-value indicates that the observation obtained is improbable given the null hypothesis and thus provides evidence against the null hypothesis.

True or False The purpose of hypothesis testing is to prove our belief for a given scenario.

True or False A Type I error is always worse than a Type II error.

True or False The alternative hypothesis, HA, contains the values of the parameter we consider plausible when we reject the null hypothesis, H0.