Refer to the following scenario to answer questions #3 through #5.

According to the most recent 2018 estimates from the U.S. Census Bureau, the average age of first marriage for women is approximately 28 years old. You think that this number is much too low. You randomly sample 12 women and conduct a single sample t test to determine whether the known value of 28 for the population is significantly different from the mean score for the sample.

Ages of women for a random sample: 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 38, 40

Question 3

What is the mean for the sample?

Question 4

What is the value of t? (round to the thousandths)

Question 5

The difference between the population mean of 28 and the mean of the sample is statistically significant at the .05 level.

Group of answer choices

True

False

Find the mean and standard deviation for the following, where possible,if not.explain why it is not.

a. x P(x) b. x P(x) c. x P(x)

0 0.1 -9 0.15 0 0.34

1 0.2 10 0.45 1 0.23

2 0.3 11 0.38 2 0.17

3 0.4   12 -0.21 3 0.26

-4 0.3

d. In a poll of 12 to 18yr. old females, conducted by theNokTerNoh!Magazine editor,Carolyn(Zleep D’Pri’D), found that 27%of them said that they expected to see a female soccer player on a team in the Men’s World Cup within 10 years. A random sample of 12 females from this age group was selected, by use of the formula;findi.P(Exactly 8 females share this view) (4pts)ii.P(Between 5-7 share this view) (6pts)

1. Hanna Properties specializes in custom-home resales in Equestrian Estates, an exclusive subdivision in Phoenix, AZ.  A random sample of nine custom homes currently listed for sale provided the following information on size and price,  Here, x denotes size, in hundreds of square feet rounded to the nearest hundred, and y denotes price, in thousands of dollars, rounded to the nearest thousand.

1. Give the simple linear regression model and assumptions.

2. Write down the least squares regression line (3 decimal places).  

3. Give the 95% confidence interval for the slope parameter.

4. Test for a significant linear relationship between x and y at the 5% significance level.  Give the hypotheses, test statistic, conclusion, and interpretation.

he city council of Pine Bluffs is considering increasing the number of police in an effort to reduce crime. Before making a final decision, the council asked the chief of police to survey other cities of similar size to determine the relationship between the number of police and the number of crimes reported. The chief gathered the following sample information. City Police Number of Crimes City Police Number of Crimes Oxford 15 17 Holgate 17 7 Starksville 17 13 Carey 12 21 Danville 25 5 Whistler 11 19 Athens 27 7 Woodville 22 6 Determine the standard error of estimate. (Round your answer to 3 decimal places.) Determine the coefficient of determination. (Round your answer to 2 decimal places.) Interpret the coefficient of determination. (Round your answer to the nearest whole number.)

1. Hanna Properties specializes in custom-home resales in Equestrian Estates, an exclusive subdivision in Phoenix, AZ.  A random sample of nine custom homes currently listed for sale provided the following information on size and price,  Here, x denotes size, in hundreds of square feet rounded to the nearest hundred, and y denotes price, in thousands of dollars, rounded to the nearest thousand.

1. Give the simple linear regression model and assumptions.

2. Write down the least squares regression line (3 decimal places).  

3. Give the 95% confidence interval for the slope parameter.

4. Test for a significant linear relationship between x and y at the 5% significance level.  Give the hypotheses, test statistic, conclusion, and interpretation.

1)      A personal director is interested in studying the relationship (if any) between age and salary. Sixteen employees are randomly selected and their age and salary are recorded.

a)      Plot the data points on a scatterplot.

b)      Determine the correlation coefficient   

c)       Describe the relationship indicated by the correlation coefficient and the scatterplot.

d)      If there is a linear relationship, find the equation of the line of regression

e)      Graph the line of regression on the same axes where you constructed the scatterplot in (a) above

f)       Use either your line of regression or the equation of the line of regression to predict salaries for Age = 50 and Age = 70.

osteoporosis is a condition in which people experience decreased bone mass and an increase in the risk of bone fracture. Actonel is a drug that helps combat osteoporosis in postmenopausal women. In clinical trials, 1374 postmenopausal women were randomly divided into experimental and control groups. The subjects in the experimental group were administered 5 milligrams of Actonal, while the subjects in the control group were administered a placebo. The number of women who experienced a bone fracture over the course of one year was recorded. Of the 696 women in the experimental group, 27 experienced a fracture during the course of the year. Of the 678 women in the control group, 49 experienced a fracture during the course of the year.

a. Does the sample evidence suggest the drug is effective in preventing bone fractures? Use the × = 0.01 level of significance.

b. Construct a 95% confidence interval for the difference between the two population proportions, p exp - p control.

You are interested in finding a 90% confidence interval for the mean number of visits for physical therapy patients. The data below show the number of visits for 12 randomly selected physical therapy patients. Round answers to 3 decimal places where possible.

a. To compute the confidence interval use a ? z t  distribution.

b. With 90% confidence the population mean number of visits per physical therapy patient is between  and   visits.

c. If many groups of 12 randomly selected physical therapy patients are studied, then a different confidence interval would be produced from each group. About  percent of these confidence intervals will contain the true population mean number of visits per patient and about  percent will not contain the true population mean number of visits per patient.

(5) Suppose x has a distribution with μ = 20 and σ = 16.

(a) If a random sample of size n = 47 is drawn, find μ_x, σ_x and P(20 ≤ x ≤ 22). (Round σ_x to two decimal places and the probability to four decimal places.)

μ_x =

σ _x =

P(20 ≤ x ≤ 22)=

(b) If a random sample of size n = 61 is drawn, find μ_x, σ_x and P(20 ≤ x ≤ 22). (Round σ_x to two decimal places and the probability to four decimal places.)

μ_x =

σ _x =

P(20 ≤ x ≤ 22)=

c) Why should you expect the probability of part (b) to be higher than that of part (a)? (Hint: Consider the standard deviations in parts (a) and (b).)
The standard deviation of part (b) is (Blank)?  part (a) because of the ( Blank) ? Sample size. Therefore, the distribution about μ_x is (Blank) ?

(8) Let x be a random variable that represents the level of glucose in the blood (milligrams per deciliter of blood) after a 12 hour fast. Assume that for people under 50 years old, x has a distribution that is approximately normal, with mean μ = 54 and estimated standard deviation σ = 11. A test result x < 40 is an indication of severe excess insulin, and medication is usually prescribed.

(a) What is the probability that, on a single test, x < 40? (Round your answer to four decimal places.)

(b) Suppose a doctor uses the average x for two tests taken about a week apart. What can we say about the probability distribution of x? Hint: See Theorem 6.1.

What is the probability that x < 40? (Round your answer to four decimal places.)

(c) Repeat part (b) for n = 3 tests taken a week apart. (Round your answer to four decimal places.)

(d) Repeat part (b) for n = 5 tests taken a week apart. (Round your answer to four decimal places.)

Explain what this might imply if you were a doctor or a nurse.

(9) Let x represent the dollar amount spent on supermarket impulse buying in a 10-minute (unplanned) shopping interval. Based on a certain article, the mean of the x distribution is about $27 and the estimated standard deviation is about $9.

(a) Consider a random sample of n = 100 customers, each of whom has 10 minutes of unplanned shopping time in a supermarket. From the central limit theorem, what can you say about the probability distribution of x, the average amount spent by these customers due to impulse buying? What are the mean and standard deviation of the x distribution?

Is it necessary to make any assumption about the x distribution? Explain your answer.

(b) What is the probability that x is between $25 and $29? (Round your answer to four decimal places.)

(c) Let us assume that x has a distribution that is approximately normal. What is the probability that x is between $25 and $29? (Round your answer to four decimal places.)

(d) In part (b), we used x, the average amount spent, computed for 100 customers. In part (c), we used x, the amount spent by only one customer. The answers to parts (b) and (c) are very different. Why would this happen?

(10) A European growth mutual fund specializes in stocks from the British Isles, continental Europe, and Scandinavia. The fund has over 325 stocks. Let x be a random variable that represents the monthly percentage return for this fund. Suppose x has mean μ = 1.4% and standard deviation σ = 1.1%.

(a) Let's consider the monthly return of the stocks in the fund to be a sample from the population of monthly returns of all European stocks. Is it reasonable to assume that x (the average monthly return on the 325 stocks in the fund) has a distribution that is approximately normal? Explain.

(Blank)  x is a mean of a sample of n = 325 stocks. By the(Blank)  the x distribution( Blank) approximately normal?

(b) After 9 months, what is the probability that the average monthly percentage return x will be between 1% and 2%? (Round your answer to four decimal places.)(c)After 18 months, what is the probability that the average monthly percentage return x will be between 1% and 2%? (Round your answer to four decimal places.

(d) Compare your answers to parts (b) and (c). Did the probability increase as n (number of months) increased? Why would this happen?

(e) If after 18 months the average monthly percentage return x is more than 2%, would that tend to shake your confidence in the statement that μ = 1.4%? If this happened, do you think the European stock market might be heating up? (Round your answer to four decimal places.)  P(x > 2%)

Explain.