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.

According to a survey in a​ country, 15 ​% of adults do not own a credit card. Suppose a simple random sample of 200 adults is obtained. Complete parts​ (a) through​ (d) below.

​(a) Describe the sampling distribution of ModifyingAbove p with caret ​, the sample proportion of adults who do not own a credit card. Choose the phrase that best describes the shape of the sampling distribution of ModifyingAbove p with caret below.

A. Approximately normal because n less than or equals 0.05 Upper N and np left parenthesis 1 minus p right parenthesis greater than or equals 10

B. Approximately normal because n less than or equals 0.05 Upper N and np left parenthesis 1 minus p right parenthesis less than 10

C. Not normal because n less than or equals 0.05 Upper N and np left parenthesis 1 minus p right parenthesis less than 10

D. Not normal because n less than or equals 0.05 Upper N and np left parenthesis 1 minus p right parenthesis greater than or equals 10 Determine the mean of the sampling distribution of ModifyingAbove p with caret . mu Subscript ModifyingAbove p with caret Baseline equals nothing ​(Round to two decimal places as​ needed.)

Determine the standard deviation of the sampling distribution of ModifyingAbove p with caret . sigma Subscript ModifyingAbove p with caret equalsnothing ​(Round to three decimal places as​ needed.)

​(b) What is the probability that in a random sample of 200 ​adults, more than 17 ​% do not own a credit​ card?

The probability is    ? (Round to four decimal places as​ needed.)

Interpret this probability.

If 100 different random samples of __ 200 adults were​ obtained, one would expect ____ to result in more than 17% not owning a credit card.

​(Round to the nearest integer as​ needed.)

​(c) What is the probability that in a random sample of 200 adults, between 12% and 17​% do not own a credit​ card?

The probability is ____? ​(Round to four decimal places as​ needed.)

Interpret this probability.

If 100 different random samples of 200 adults were​ obtained, one would expect ____ to result in between 12% and 17% not owning a credit card.

​(Round to the nearest integer as​ needed.)

​(d) Would it be unusual for a random sample of 200 adults to result in 24 or fewer who do not own a credit​ card? Why? Select the correct choice below and fill in the answer box to complete your choice.

​(Round to four decimal places as​ needed.)

A.The result is not unusual because the probability that ModifyingAbove p with caret is less than or equal to the sample proportion is ___ which is greater than​ 5%.

B.The result isunusual because the probability that ModifyingAbove p with caret is less than or equal to the sample proportion is _____ which is less than​ 5%.

C.The result is notunusual because the probability that ModifyingAbove p with caretis less than or equal to the sample proportion is _____ which is less than​ 5%.

D.The result is unusual because the probability that ModifyingAbove p with caret is less than or equal to the sample proportion is _____ which is greaterthan​ 5%.

Suppose a mutual fund qualifies as having moderate risk if the standard deviation of its monthly rate of return is less than 3​%. A​ mutual-fund rating agency randomly selects 24 months and determines the rate of return for a certain fund. The standard deviation of the rate of return is computed to be 2.68​%. Is there sufficient evidence to conclude that the fund has moderate risk at the alpha equals 0.01 level of​ significance? A normal probability plot indicates that the monthly rates of return are normally distributed.

X^2 = ? (Round to three decimal places as needed.)

Use technology to determine the P-value for the test statistic

What is the correct conclusion at the a = 0.01 level of significance?

10. In a study conducted to determine whether the role that sleep disorders play in academic performance, researcher conducted a survey of 1800 college students to determine if they had a sleep disorder. Of the 500 students with a sleep disorder, the mean GPA was 2.51 with a standard deviation of 0.85. Of the 1300 students without a sleep disorder, the mean GPA is 2.85 with a standard deviation of 0.78. Test the claim that sleep disorder adversely affects one’s GPA at the 0.05 level of significance?

11. In one experiment, the participant must press a key on seeming a blue screen and reaction time (in seconds) to press the key is measured. The same person is then asked to press a key on seeing a red screen, again with reaction time measured. The results for six randomly sampled study participants are as follows:

Participant

1

2

3

4

5

6

Blue

0.582

0.481

0.841

0.267

0.685

0.450

Red

0.408

0.407

0.542

0.402

0.456

0.522

Construct a 99% confidence interval about the population mean difference. Assume the differences are approximately normally distributed.

HOMEWORK 3 (part3):

3) You now wish to concern yourself with a comparison of the proportions of the supporters of the candidate based upon gender concerning their assertions of party loyalty. Specifically, you wish to know whether the proportion of men that supports the candidate that describes itself as party loyalists is less than the proportion of women that feels the same. The sample data concerning whether the supporter describes himself or herself as a party loyalist is also shown in appendix two below. At both the 2% and 5% levels of significance, is the proportion of male supporters that describes itself as party loyalists less than the proportion of female supporters of the candidate that describes itself as party loyalists? If the procedure you have chosen for this problem allows it (using PHStat) to construct confidence intervals for the difference in the proportions of male and female supporters that describes itself as party loyalists, construct 98% and 95% confidence intervals for the difference in the proportions, and explain their meanings in the context of the problem.

Appendix Two:

Male Supporter Loyalty? (Y = party loyalist, N = not a party loyalist)

Y   N         Y         Y         Y         N         Y         N         Y         N         Y         N

Y   Y         Y         Y         Y         Y         Y         Y         N         Y         Y         Y

Y   Y         N         Y         Y         Y

Female Supporter Loyalty? (Y = party loyalist, N = not a party loyalist)

Y   Y         Y         Y         N         Y         N         Y         Y         Y         N         Y

Y   Y         N         Y         Y         Y         Y         Y         Y         Y         Y         Y

Y   Y         Y         Y         Y         Y

Suppose that you are testing the hypotheses H0​: p=0.18 vs. HA​: p=/ 0.18. A sample of size 150 results in a sample proportion of 0.25.

​a) Construct a 99​% confidence interval for p. ​

b) Based on the confidence​ interval, can you reject H0 at a =0.01​? Explain.

​c) What is the difference between the standard error and standard deviation of the sample​ proportion?

​d) Which is used in computing the confidence​ interval?

The average time to run the 5K fun run is 20 minutes and the standard deviation is 2.4 minutes. 8 runners are randomly selected to run the 5K fun run. Round all answers to 4 decimal places where possible and assume a normal distribution.

What is the distribution of X X ? X X ~ N(,)

What is the distribution of ¯ x x¯ ? ¯ x x¯ ~ N(,)

What is the distribution of ∑ x ∑x ? ∑ x ∑x ~ N(,)

If one randomly selected runner is timed, find the probability that this runner's time will be between 20.3272 and 21.1272 minutes. For the 8 runners, find the probability that their average time is between 20.3272 and 21.1272 minutes.

Find the probability that the randomly selected 8 person team will have a total time more than 152.8.

For part e) and f), is the assumption of normal necessary? NoYes

The top 15% of all 8 person team relay races will compete in the championship round. These are the 15% lowest times. What is the longest total time that a relay team can have and still make it to the championship round? minutes