A group of five individuals with high blood pressure were given a new drug that was designed to lower blood pressure. Systolic blood pressure was measured before and after treatment for each individual, with the following results:

Let μX represent the population mean before treatment and let μY represent the population mean after treatment. Find a 90% confidence interval for the difference μD=μX−μY . Round the answers to three decimal places.

The 90% confidence interval is

A magazine reported the mean annual household income of its readers to be $150,000 with a standard deviation of $30,000. A recent sample of 80 households from among those subscribing to this magazine found a mean of $139,155. What is the upper bound of a 95% confidence interval for the mean income (correct to no decimal places)?

As in exercise 3 Cholesterol levels in health us adults average about 215mg/Dl with a Standard deviation of about 30 mg /dl and are roughly normally distributed If the cholestrol levels of a sample of 42 healthy us adults is taken what is the probablility that the mean cholesterol level of the sample

A. will be no more than 215?

b. will be between 205 and 225

c. Will be less than 200?

d. Will be greater than 220?

The percentage of income spent on housing (including mortgage/rent, taxes, utilities) is an important factor loan agents use in approving customers for mortgages. A researched selected a sample of 20 homeowners in Florida and calculated their total housing costs are a percent of their monthly income. The researcher collected this information from the same 20 homeowners 5 years ago and again in 2019. The information collected is in the attached Excel data file. Is it reasonable to conclude the percent is less now than five years ago? Use a two-sample test of hypothesis to determine your answer. Explain and show your work, including the 6 steps for hypothesis testing.

2. Let X ~ Pois (λ) λ > 0

a. Show explicitly that this family is “very regular,” that is, that R0,R1,R2,R3,R4 hold.

R 0 - different parameter values have different functions.

R1 - parameter space does not contain its own endpoints.

R 2. - the set of points x where f (x, λ) is not zero and should not depend on λ .

R 3. One derivative can be found with respect to λ.

R 4. Two derivatives can be found with respect to λ.

b. Find the maximum likelihood estimator of λ, call it Yn for this problem.

c. Is Yn unbiased? Explain.

d. Show that Yn is consistent asymptotically normal and identify the asymptotic normal variance.

e. Variance-stabilize your result in (d) or show there is no need to do so.

f. Compute I (λ) where I is Fisher’s Information.

g. Compute the efficiency of Yn for λ (or show that you should not!).

1) A grocery store carries the following items. There are two main categories of food – conventional and organic ingredients – and four food groups. The data are shown in the following table. Food Groups Food Categories Grains Fruits Vegetables Meat Total Conventional 82 48 276 204 610 Organic 93 77 24 11 205 Total 175 125 300 215 815 If all of the grains and meats were accidentally displayed together without a sticker or label to mark their origin, what is the probability that you select a grain or meat that is conventional into your grocery basket? First compute for yourself the row (i.e., n1+, n2+), column (i.e., n+1, n+2, n+3, n+4), and overall (i.e., n++) totals, to aid in answering the question. Answer:

2) Suppose at random 39% of school children develop nausea and vomiting following holiday parties and that you conduct a study to examine this phenomenon, with a sample size of n=12. What is the probability that between more than 6 and 10 or less children become sick?

3)

A grocery store carries the following items. There are two main categories of food – conventional and organic ingredients – and four food groups. The data are shown in the following table.

If all of the items were accidentally displayed together without a sticker or label to mark their origin, what is the probability that you select an organic grain, vegetable, or meat in your grocery basket? First compute for yourself the row (i.e., n₁₊, n₂₊), column (i.e., n₊₁, n₊₂, n₊₃, n₊₄), and overall (i.e., n₊₊) totals, to aid in answering the question.

Answer:

A survey of several 9 to 11 year olds recorded the following amounts spent on a trip to the mall: $22.91,$17.13,$13.60 Construct the 99% confidence interval for the average amount spent by 9 to 11 year olds on a trip to the mall. Assume the population is approximately normal. Step 3 of 4 : Find the critical value that should be used in constructing the confidence interval. Round your answer to three decimal places.

Assume that a winning ticket is one which matches the 6 numbers drawn from 1 to 49.
(a) (1 mark) Suppose p is the probability of winning the grand prize. Write down the value for p for
Lotto 649.
(b) (1 mark) Write down the probability of winning (for the first time) on the nth draw (i.e. losing
on the first n − 1 draws).
(c) (1 mark) Determine the expected number of draws you must play (1 ticket each draw) before
winning for the first time.
(d) (1 mark) Show how the average time to win Lotto 649 when playing 1 ticket per weekly 649 draw
turns into the long wait given for the Homo sapiens example.

How can the use of linear equations and inequalities assist you with linear regression to make predictions?

There is some evidence that, in the years 1981-85, a simple name change resulted in a short-term increase in the price of certain business firms' stocks (relative to the prices of similar stocks). (See D. Horsky and P. Swyngedouw, "Does it pay to change your company's name? A stock market perspective," Marketing Science v.6, pp. 320-35,1987.) Suppose that, to test the profitability of name changes in the more recent market (the past five years), we analyze the stock prices of a large sample of corporations shortly after they changed names, and we find that the mean relative increase in stock price was about 0.89%, with a standard deviation of 0.16%. Suppose that this mean and standard deviation apply to the population of all companies that changed names during the past five years. Complete the following statements about the distribution of relative increases in stock price for all companies that changed names during the past five years.

(a) According to Chebyshev's theorem, at least of the relative increases in stock price lie between 0.57 % and 1.21 %.

(b) According to Chebyshev's theorem, at least of the relative increases in stock price lie between 0.65 % and 1.13 %.

(c) Suppose that the distribution is bell-shaped. According to the empirical rule, approximately of the relative increases in stock price lie between 0.57 % and 1.21 %. (d) Suppose that the distribution is bell-shaped. According to the empirical rule, approximately 99.7% of the relative increases in stock price lie between % and %.

pediatrician wants to determine the relation that may exist between a​ child's height and head circumference. She randomly selects 5 children and measures their height and head circumference. The data are summarized below. Complete parts​ (a) through​ (f) below. Height​ (inches), x 27 25.5 27.75 25 26.5 Head Circumference​ (inches), y 17.5 17.1 17.6 16.9 17.3 ​(a) Treating height as the explanatory​ variable, x, use technology to determine the estimates of beta 0 and beta 1. beta 0 almost equalsb 0 equals ???????? ​(Round to four decimal places as​ needed.) beta 1almost equalsb 1equals nothing ​(Round to four decimal places as​ needed.) (b) Use technology to compute the standard error of the​ estimate, s Subscript e. s Subscript eequals ????​(Round to four decimal places as​ needed.) ​(c) A normal probability plot suggests that the residuals are normally distributed. Use technology to determine s Subscript b 1. s Subscript b 1equals ??????   ​(Round to four decimal places as​ needed.) ​(d) A normal probability plot suggests that the residuals are normally distributed. Test whether a linear relation exists between height and head circumference at the alphaequals0.01 level of significance. State the null and alternative hypotheses for this test. Choose the correct answer below. A. Upper H 0​: beta 0equals0 Upper H 1​: beta 0not equals0 B. Upper H 0​: beta 0equals0 Upper H 1​: beta 0greater than0 C. Upper H 0​: beta 1equals0 Upper H 1​: beta 1not equals0 Your answer is correct.D. Upper H 0​: beta 1equals0 Upper H 1​: beta 1greater than0 Determine the​ P-value for this hypothesis test. ​P-valueequals ????? ​(Round to three decimal places as​ needed.) What is the conclusion that can be​ drawn? A. Do not reject Upper H 0 and conclude that a linear relation does not exist between a​ child's height and head circumference at the level of significance alphaequals0.01. B. Reject Upper H 0 and conclude that a linear relation does not exist between a​ child's height and head circumference at the level of significance alphaequals0.01. C. Do not reject Upper H 0 and conclude that a linear relation exists between a​ child's height and head circumference at the level of significance alphaequals0.01. D. Reject Upper H 0 and conclude that a linear relation exists between a​ child's height and head circumference at the level of significance alphaequals0.01. ​(e) Use technology to construct a​ 95% confidence interval about the slope of the true​ least-squares regression line. Lower​ bound: ???? Upper​ bound: ????? ​(Round to three decimal places as​ needed.) ​(f) Suppose a child has a height of 26.5 inches. What would be a good guess for the​ child's head​ circumference? A good estimate of the​ child's head circumference would be ???????? ​(Round to two decimal places as​ needed.)

1. Which of the following z-scores is located furthest AND below the mean of a distribution?

a.z = -3.0

b.z = -1.0

c.z = +1.0

d.z = +3.0

2. All of the following apply to the concept of variability EXCEPT:

a.it is a form of inferential statistics

b.it is a form of descriptive statistics

c.it measures the extent to which scores deviate from the mean

d.it measures distance/spread of scores in a distribution

3. Which statement best describes the concept of a z-score?

a.they standardize a distribution, but do not provide any information about location

b.they standardize a distribution and allow for comparisons between different distributions

c.they standardize a distribution and are always equal to raw scores

d.they do not standardize a distribution, but do provide information about location

4.What does the Unit Normal Table tell you about a distribution?

a.the standardized proportions of a normal distribution corresponding to raw scores

b.the standardized proportions of a skewed distribution corresponding to raw scores

c.the standardized proportions of a normal distribution corresponding to z-scores

d.the standardized proportions of a skewed distribution corresponding to z-scores

5.With respect to probability and sampling:

a.each individual in a population should have an equal chance of being selected for a sample

b.sampling should occur with replacement

c.both answers a and b

d.none of the above

27. Chapter 7: Question 27

Which statement best defines the concept of the distribution of sample means?

a.it is a distribution of all the possible means of a specified (n) taken from a population

b.it is a distribution of sample statistics (a sampling distribution)

c.it is a distribution of all the possible raw scores taken from a population

d.both answers a and b

29. Chapter 7: Question 29

All of the following are characteristics of a distribution of sample means EXCEPT:

a.sample means should occur mostly near this distribution's mean

b.with larger n's, this distribution becomes more variable

c.with smaller n's, this distribution becomes more variable

d.all of the above

31.) Hypothesis testing is a form of _________, which uses _________ data to evaluate a hypothesis about a _________.

            a. descriptive statistics; population; sample

            b. inferential statistics; population; sample

            c. inferential statistics; sample; population

            d. descriptive statistics; sample; population

33.Which of the following is true about the concept of statistical power?

a.it is a useless piece of information with respect to hypothesis testing

b.it is the probability that a hypothesis test will erroneously reject a true null hypothesis

c.it is the probability that a hypothesis test will correctly reject a false null hypothesis

d.it is also known as Type I Error (?)

35.) Which of the following does NOT apply to Type II Errors?

            a. Type II Error influences the power of a hypothesis test

            b. they occur when a researcher fails to reject a false null hypothesis

            c. the probability of a Type II Error is known as beta (β)

            d. all of the above apply

36. Chapter 9: Question 36

Under which conditions will it be very difficult to detect a treatment effect using the t-statistic?

a.with a small sample size and low sample variance

b.with a small sample size and high sample variance

c.with a large sample size and high sample variance

d.with a large sample size and low sample variance

37. Chapter 9: Question 37

All of the following are assumptions of the one-sample t-test EXCEPT:

a.scores come from independent observations

b.the population that is sampled is skewed

c.the population that is sampled is normal

d.none of the above (all of the above are assumptions)

39. Chapter 9: Question 39

What is the term for the estimated standard distance between a sample mean (M) and the population mean (u)?

a.estimated standard variance

b.estimated standard deviation

c.estimated standard error

d.estimated standard treatment effect

You wish to test the following claim ( H a ) at a significance level of α = 0.001 . H o : p 1 = p 2 H a : p 1 < p 2 You obtain 22.7 % successes in a sample of size n 1 = 775 from the first population. You obtain 26.7 % successes in a sample of size n 2 = 795 from the second population.

Calculator tip test statistic = What is the p-value for this sample? p-value =

The p-value is... less than (or equal to) α greater than α This test statistic leads to a decision to...

reject the null accept the null fail to reject the null As such, the final conclusion is that...

There is sufficient evidence to warrant rejection of the claim that the first population proportion is less than the second population proportion.

There is not sufficient evidence to warrant rejection of the claim that the first population proportion is less than the second population proportion.

The sample data support the claim that the first population proportion is less than the second population proportion. There is not sufficient sample evidence to support the claim that the first population proportion is less than the second population proportion.

concrete​ cures, it gains strength. The following data represent the​ 7-day and​ 28-day strength in pounds per square inch​ (psi) of a certain type of concrete. Complete parts​ (a) through​ (f) below. ​7-Day Strength​ (psi), x 2480 3330 2620 3380 3390 ​28-Day Strength​ (psi), y 4120 4850 4190 5020 5220 ​(a) Treating the​ 7-day strength as the explanatory​ variable, x, use technology to determine the estimates of beta 0 and beta 1. beta 0almost equalsb 0equals nothing ​(Round to one decimal place as​ needed.) beta 1almost equalsb 1equals nothing ​(Round to four decimal places as​ needed.) ​28-Day Strength​ (psi), y ​(a) Treating the​ 7-day strength as the explanatory​ variable, x, use technology to determine the estimates of beta 0 and beta 1. beta 0almost equalsb 0equals Round to one decimal place as​ needed.) beta 1almost equalsb 1equals Round to four decimal places as​ needed.) ​(b) Compute the standard error of the​ estimate, s Subscript e. s Subscript eequals ​(Round to one decimal place as​ needed.) ​(c) A normal probability plot suggests that the residuals are normally distributed. Determine s Subscript b 1. Use the answer from part ​(b). s Subscript b 1equals 0.1212   ​(Round to four decimal places as​ needed.) ​(d) A normal probability plot suggests that the residuals are normally distributed. Test whether a linear relation exists between​ 7-day strength and​ 28-day strength at the alphaequals0.05 level of significance. State the null and alternative hypotheses. Choose the correct answer below. A. Upper H 0​: beta 1equals0 Upper H 1​: beta 1not equals0 Your answer is correct.B. Upper H 0​: beta 0equals0 Upper H 1​: beta 0not equals0 C. Upper H 0​: beta 0equals0 Upper H 1​: beta 0greater than0 D. Upper H 0​: beta 1equals0 Upper H 1​: beta 1greater than0 Determine the​ P-value of this hypothesis test. ​P-valueequals Round to three decimal places as​ needed.) What is the conclusion that can be​ drawn? A. Do not reject Upper H 0 and conclude that a linear relation does not exist between the​ 7-day and​ 28-day strength of a certain type of concrete at the alphaequals0.05 level of significance. B. Reject Upper H 0 and conclude that a linear relation does not exist between the​ 7-day and​ 28-day strength of a certain type of concrete at the alphaequals0.05 level of significance. C. Do not reject Upper H 0 and conclude that a linear relation exists between the​ 7-day and​ 28-day strength of a certain type of concrete at the alphaequals0.05 level of significance. D. Reject Upper H 0 and conclude that a linear relation exists between the​ 7-day and​ 28-day strength of a certain type of concrete at the alphaequals0.05 level of significance. Your answer is correct. ​(e) Construct a​ 95% confidence interval about the slope of the true​ least-squares regression line. Lower​ bound: ​(Round to three decimal places as​ needed.) Upper​ bound: ​(Round to three decimal places as​ needed.) ​(f) What is the estimated mean​ 28-day strength of this concrete if the​ 7-day strength is 3000​ psi? A good estimate of the mean​ 28-day strength is 4740.81 psi. ​(Round to two decimal places as​ needed.)