The risk of females experiencing an anxiety disorder during a given 12-month period is approximately 1 in 5. Suppose a researcher plans to take a random sample of females and monitor their anxiety over 12 months.

If 10 females are randomly sampled, what is the probability that 5 or more will experience an anxiety disorder? (Round answer to 3 decimal places)

If 20 females are randomly sampled, what is the probability that 2 or more will experience an anxiety disorder? (Round answer to 3 decimal places)

If 20 females are randomly sampled, what is the probability that 5 or less will experience an anxiety disorder? (Round answer to 3 decimal places)

If 30 females are randomly sampled, what is the probability that 10 or less will experience an anxiety disorder? (Round answer to 3 decimal places)

Majesty Video Production Inc. wants the mean length of its advertisements to be 24 seconds. Assume the distribution of ad length follows the normal distribution with a population standard deviation of 2 seconds. Suppose we select a sample of 15 ads produced by Majesty. a. What can we say about the shape of the distribution of the sample mean time? b. What is the standard error of the mean time? c. What percent of the sample means will be greater than 25.50 seconds? d. What percent of the sample means will be greater than 22.50 seconds? e. What percent of the sample means will be greater than 22.50 but less than 25.50 seconds?

An interactive poll found that 318 of 2,308 adults aged 18 or older have at least one tattoo.

​(a) Obtain a point estimate for the proportion of adults who have at least one tattoo.

​(b) Construct a 90% confidence interval for the proportion of adults with at least one tattoo.

(c) Construct a 98% confidence interval for the proportion of adults with at least one tattoo.

​(d) What is the effect of increasing the level of confidence on the width of the​ interval?

Let x represent the average annual salary of college and university professors (in thousands of dollars) in the United States. For all colleges and universities in the United States, the population variance of x is approximately σ² = 47.1. However, a random sample of 16 colleges and universities in Kansas showed that x has a sample variance s² = 79.1. Use a 5% level of significance to test the claim that the variance for colleges and universities in Kansas is greater than 47.1. Find a 95% confidence interval for the population variance.

(a) What is the level of significance?


State the null and alternate hypotheses.

H_o: σ² = 47.1; H₁: σ² < 47.1H_o: σ² < 47.1; H₁: σ² = 47.1    H_o: σ² = 47.1; H₁: σ² ≠ 47.1H_o: σ² = 47.1; H₁: σ² > 47.1

(b) Find the value of the chi-square statistic for the sample. (Round your answer to two decimal places.)


What are the degrees of freedom?


What assumptions are you making about the original distribution?

We assume a binomial population distribution.We assume a exponential population distribution.    We assume a uniform population distribution.We assume a normal population distribution.

(c) Find or estimate the P-value of the sample test statistic.

P-value > 0.1000.050 < P-value < 0.100    0.025 < P-value < 0.0500.010 < P-value < 0.0250.005 < P-value < 0.010P-value < 0.005

(d) Based on your answers in parts (a) to (c), will you reject or fail to reject the null hypothesis?

Since the P-value > α, we fail to reject the null hypothesis.Since the P-value > α, we reject the null hypothesis.    Since the P-value ≤ α, we reject the null hypothesis.Since the P-value ≤ α, we fail to reject the null hypothesis.

(e) Interpret your conclusion in the context of the application.

At the 5% level of significance, there is insufficient evidence to conclude the variance of annual salaries is greater in Kansas.At the 5% level of significance, there is sufficient evidence to conclude the variance of annual salaries is greater in Kansas.    

(f) Find the requested confidence interval for the population variance. (Round your answers to two decimal places.)

Interpret the results in the context of the application.

We are 95% confident that σ² lies above this interval.We are 95% confident that σ² lies outside this interval.    We are 95% confident that σ² lies below this interval.We are 95% confident that σ² lies within this interval.

The personnel department of ZTel, a large communications company, is reconsidering its hiring policy. Each applicant for a job must take a standard exam, and the hire or no-hire decision depends at least in part on the result of the exam. The scores of all applicants have been examined closely. They are approximately normally distributed with mean 500 and standard deviation 50. The current hiring policy occurs in two phases. The 1st phase separates all applicants into three categories: automatic accepts, automatic rejects, and maybes. The automatic accepts are those whose test scores are 600 or above. The automatic rejects are those whose test scores are 420 or below. All other applicants (the maybes) are passed on to a 2nd phase where their previous job experience, special talents, and other factors are used as hiring criteria. To calculate the percentage of applicants who are automatic accepts, given the current standards, which of the following functions should be entered in EXCEL?

Briefly describe the difference between the model selection critria Cp, AIC, BIC, and R2 adj . For each of them, also give examples when one is preferred over the others.

In a large accounting firm, the proportion of accountants with MBA degrees and at least five years of professional experience is 70% as large as the proportion of accountants with no MBA degree and less than five years of professional experience. Furthermore, 20% of the accountants in this firm have MBA degrees, and 26% have fewer than five years of professional experience. If one of the firm’s accountants is selected at random, what is the probability that this accountant has no MBA degree AND less than five years of professional experience?

1. What is the mean and standard deviation associated with the standard normal distribution?

2. Use the standard normal distribution table to calculate the following probabilities

A) P (z ≤ -1.64)

B) P (z ≤ 2.11)

C) P (z ≥ 0.73)

D) P (-1.31 ≤ z ≤ -0.32)

3. Use the standard normal distribution table to find the z-value for each of the following

A) P (z ≤ ?) = 0.9495

B) P (z ≤ ?) = 0.2810

C) P (z ≥ ?) = 0.9968

D) P ( -1.13 ≤ z ≤ ?) = 0.8299

4. A local grocery store owner wants to learn more about how many apples patrons buy from his store week to week, and he has asked for your help calculating some probabilities. He tells you that he believes the data to be normally distributed, and that the average amount of apples bought each week is 678.32 lbs. with a standard deviation of 53.98 lbs.

A) What is the probability that the store sells more than 750 lbs. of apples in a week?

B) What is the probability that the store sells less than 500 lbs. of apples in a week?

C) What is the probability that the store sells between 600 and 700 lbs. of apples?

D) What is the probability that the store sells exactly 678.32 lbs. of apples?

The score of a course out of 100 in Winter of 10 students are 48, 92, 47, 44, 94, 18, 95, 67, 74, 64

a. Calculate Q1, Q3 and IQR of the data.

b. Find the mean, median and standard deviation

c. Determine whether the smallest value of this data set is an outlier.

d. Comment the shape of the distribution.

1. Given the following information, would your decision be to reject or fail to reject the null hypothesis? In addition, briefly explain what your decision means for the research problem. Keep in mind that the level of significance is .05.
2. 1. The null hypothesis that there is a no relationship between the number of hours worked and job satisfaction (p = .51).

1. Let X be a random variable that represents the weights in kilograms (kg) of a healthy adult female deer (doe) from Mesa Verde National Park. X has a distribution that is approximately normal with µ = 63.0 kg and standard deviation σ = 7.1 kg. A doe is considered to be malnourished if it weighs less than 54 kg.

a. If the doe population is healthy, what is the probability that a single doe captured weighs less than 54 kg?

b. What is the probability that the mean weight of a random sample of 50 does is less than 54 kg?

c. Create a 95% confidence interval for the mean weight of a random sample of 36 does in Mesa Verde National Park.

2. A CPA firm is auditing the accounts of a large interstate banking system. Out of a random sample of 152 accounts, it was found that 19 had transaction errors. Let p be the number of accounts with transaction errors.

a. Find a point estimate for p ( pˆ ):

b. Find a 99% confidence interval for p: . An article in the local paper claims that the average amount spent in a visit to a fast food restaurant is $20. Is the fast food restaurant in problem #1 unusually inexpensive? (In other words, are people spending less at the local fast food restaurant than the population does at an average fast food restaurant?) Assuming that the amount people spend is normally distributed, conduct a hypothesis test using a 5% significance level. a. Ho: Ha: b. Is this a right-tailed, two-tailed or left-tailed test?

c. Compute the z or t test statistic. Show the correct computation.

d. Find the p-value for the test statistic. e. Based on your answers above, do you reject or fail to reject the null hypothesis? What do you conclude about the average cost of this fast food restaurant?

24. A business claims that no more than 1.2% of all its products do not meet the minimum government standards. A survey of 450 products revealed that 10 did not meet the standards. If the level of significance is 0.02, what should be the decision in the test?

A. Reject the null hypothesis, and agree that more than 1.2% of products fail to meet government standards.

B. There is insufficient evidence to reject the null hypothesis.

C. Do not reject the null hypothesis, and agree that no more than 1.2% of products fail to meet government standards.

D. Information is insufficient for finding the critical value of the test, thus no decision can be made.

6. There are 40 books on a bookshelf. Exactly 10 of them have a red cover. The remaining books have a white cover. You intend to choose a random sample of nine books, but you haven't decided whether to choose with replacement or without replacement?

a) If you choose books with our placement, would this procedure lead to independent trials or dependent trials?

b)if you choose books with replacement, would this procedure be consistent with a binomial experiment or not?

c) what is the size of the population? show your work

d) what is the size of the sample? show your work

e) if you ultimately conduct a binomial experiment, find the probability that the 5th book you select, happens to have a red cover? please show your work

f) if you ultimately conduct a binomial experiment, find the probability that you choose two or more red-covered books? please show your work

Finally, for a binomial experiment, please determine: show your work

1. average number of red books, per sample of nine books?
2. the variance of the number of red books, per sample of nine books?

4. A statistical researcher wishes to investigate the relationship between a student’s study time and their ultimate exam grade for that exam. The following data is determined:

Ex=40     Ex²=354          and Exy=670

Ey=80      Ey²=1346

1. Sketch the scatter diagram. Does the trend appear to be positive or negative?
2. given that E(x-xbar)²=34, Please use that comment to help determine the sample standard deviation for the X data.
3. Given that [n*Ey²-(Ey)²]=330, Please use that comment to help determine the sample standard deviation for the Y data. explain
4. Please determine the regression equation “y=a+bx” for these data. explain
5. Please use your Part D regression equation to predict the exam grade for the sixth student who happened to take 10 hours to study for the exam. explain
6. please determine the sample linear correlation coefficient for this data. explain

A study is conducted to assess whether residents in City A spent a different out-of-pocket amount on prescription medications from residents in City B last year. The study is restricted to residents who are 50 years of age or older. Residents are selected at random. For each resident, the total amount of dollars spent on prescription medications over the last year is recorded. The summary statistics of the sample data are given in the table below. Let µ1 be the mean out-of-pocket amount that residents in City A spent, and µ2 be the mean out-of-pocket amount that residents in City B spent. Run a two-sample t-test assuming equal variances. Use a significance level of 0.05. City Sample size Sample mean Sample standard deviation A 37 421 37 B 55 380 39

a. Write down the null hypothesis.

b. Write down the alternative hypothesis.

c. Calculate the point estimate for µ1 − µ2. (5 points) d. Calculate the pooled sample variance.

e. Calculate the standard error of the point estimate in c. (10 points) f. Calculate the test statistic. (10 points) g. Find out the critical value.

h. Is there a statistically significant difference in the out-of-pocket amount spent on prescription medications between City A and City B?