Let Y denote a random variable that has a Poisson distribution with mean λ = 6. (Round your answers to three decimal places.)

(a) Find P(Y = 9).

(b) Find P(Y ≥ 9).

(c) Find P(Y < 9).

(d) Find P(Y ≥ 9|Y ≥ 6).

The manager of a resort hotel stated that the mean guest bill for a weekend is $600 or less. A member of the hotel's accounting staff noticed that the total charges for guest bills have been increasing in recent months. The accountant will use a sample of future weekend guest bills to test the manager's claim.

(a)

Which form of the hypotheses should be used to test the manager's claim? Explain.

H₀: μ ≥ 600

H_a: μ < 600

H₀: μ ≤ 600

H_a: μ > 600

H₀: μ = 600

H_a: μ ≠ 600

A) The hypotheses H₀: μ ≥ 600 and H_a: μ < 600 should be used because the accountant wants to test the manager's claim that the mean guest bill μ is greater than or equal to 600 and find evidence to support μ < 600.

B)The hypotheses H₀: μ ≤ 600 and H_a: μ > 600 should be used because the accountant wants to test the manager's claim that the mean guest bill μ is less than or equal to 600 and find evidence to support μ > 600.   

C)The hypotheses H₀: μ = 600 and H_a: μ ≠ 600 should be used because the accountant wants to test the manager's claim that the mean guest bill μ is equal to 600 and find evidence to support μ ≠ 600.

(b)

What conclusion is appropriate when

H₀

cannot be rejected?

A)We are able to conclude that the manager's claim is wrong. We can conclude that μ = 600.

B)We are not able to conclude that the manager's claim is wrong.We cannot conclude that μ > 600.    

C) We are not able to conclude that the manager's claim is wrong. We cannot conclude that μ ≠ 600.

D) We are able to conclude that the manager's claim is wrong. We can conclude that μ ≤ 600.

E) We are not able to conclude that the manager's claim is wrong. We can conclude that μ ≥ 600.

(c)

What conclusion is appropriate when

H₀

can be rejected?

A) We are not able to conclude that the manager's claim is wrong. We can conclude that μ < 600.

B) We are not able to conclude that the manager's claim is wrong. We can conclude that μ > 600.    

C) We are able to conclude that the manager's claim is wrong. We can conclude that μ < 600.

D)We are able to conclude that the manager's claim is wrong. We can conclude that μ ≠ 600.

E) We are able to conclude that the manager's claim is wrong. We can conclude that μ > 600.

Health Rights Hotline published the results of a survey of 2,400 people in Northern California in which consumers were asked to share their complaints about managed care. The number one complaint was denial of care, with 17% of the participating consumers selecting it. Several other complaints were noted, including inappropriate care (14%), customer service (14%), payment disputes (11%), specialty care (10%), delays in getting care (8%), and prescription drugs (7%). These complaint categories are mutually exclusive. Assume that the results of this survey can be inferred to all managed care consumers. If a managed care consumer is randomly selected, determine the following probabilities:

1. The consumer complains about payment disputes or specialty care.
2. The consumer complains about prescription drugs and customer service.
3. The consumer complains about inappropriate care given that the consumer complains about specialty care.
4. The consumer does not complain about delays in getting care nor does the consumer complain about payment disputes.

Question 27 options:

A researcher selects a sample of n = 25 from a normal population with µ = 80 and σ = 20. If the treatment is expected to increase scores by 6 points, what is the power of a two-tailed hypothesis test using α = .05?

Enter the result for each step below:

Step 1: Enter the standard error, σ_M (enter a number with 5 decimal places using only the keys "0-9" and "."):

Step 2: Enter the z-score that marks the boundary of the positive critical region under the null hypothesis (hint, if you drew out the distribution, the boundary marks the beginning of the shaded area on the right side) (enter a positive number with 5 decimal places using only the keys "0-9" and "."):

Step 3: What is the smallest sample mean that would fall within the positive critical region defined by the boundary you entered in the last blank (enter a number with 5 decimal places using only the keys "0-9" and ".")?

Step 4: Enter the z-score that would correspond to the sample mean you entered in the previous blank under the alternative hypothesis (enter a number with 5 decimalplaces using only the keys "0-9" and "."):

Final Answer: Enter the statistical power implied by the z-score from the previous blank as a proportion (e.g., 0.5111 not 51.11%) (enter a number with 5 decimalplaces using only the keys "0-9" and "."):

Describe a test of significance on the mean of a population by stating
1. a population,
2. a quantitative variable on that population,
3. the population standard deviation of that variable (with units),
4. a null hypothesis,
5. an alternative hypothesis,
6. an α-level,
7. a sample size, and
8. a sample mean of that variable (with units). Find
9. the one-sample z-statistic and either
10. reject or fail to reject the null hypothesis. What does this tell us about the population? You do not need to list the values of the variable for individuals in either the sample or the population, and the values for 3, 4, 5, 6, 7, and 8 do not need to be calculated, only stated.

To what extent do syntax textbooks, which analyze the structure of sentences, illustrate gender bias? A study of this question sampled sentences from 10 texts. One part of the study examined the use of the words "girl," "boy," "man," and "woman." We will call the first two words juvenile and the last two adult. Is the proportion of female references that are juvenile (girl) equal to the proportion of male references that are juvenile (boy)? Here are data from one of the texts:

(a) Find the proportion of juvenile references for females and its standard error. Do the same for the males. (Round your answers to three decimal places.)

(b) Give a 90% confidence interval for the difference. (Do not use rounded values. Round your final answers to three decimal places.)

(c) Use a test of significance to examine whether the two proportions are equal. (Use p̂_F − p̂_M. Round your value for z to two decimal places and round your P-value to four decimal places.)

State your conclusion.

There is sufficient evidence to conclude that the two proportions are different.

There is not sufficient evidence to conclude that the two proportions are different.    

QUESTION 3 There are 8,000 students at the School of Management, UT Dallas. The average age of all the students is 25 years with a standard deviation of 5.1 years. A random sample of 36 students is selected. Compute the expected value of the sample mean. 5 points

QUESTION 4 There are 8,000 students at the School of Management, UT Dallas. The average age of all the students is 24 years with a standard deviation of 25.5 years. A random sample of 55 students is selected. Compute the standard deviation of the sample mean. 5 points

QUESTION 5 There are 8,000 students at the School of Management, UT Dallas. The average age of all the students is 24 years with a standard deviation of 3.81 years. What is the smallest sample size such that the standard deviation of the sample mean is 0.5 years or less? (Enter an integer number.) 10 points

QUESTION 6 There are 8,000 students at the School of Management, UT Dallas. The average age of all the students is 24 years with a standard deviation of 3 years. A random sample of 36 students is selected. What is the probability that the sample mean will be less than 24.88 years? 10 points

QUESTION 7 There are 8,000 students at the School of Management, UT Dallas. The average age of all the students is 24 years with a standard deviation of 3 years. A random sample of 36 students is selected. What is the probability that the sample mean will be greater than 23.22 years?

Lyft has recently launched “Lyft Scooters” in various cities across the U.S. Imagine the company selects two individuals, Zahra in Madison, Wisconsin, and Mateo in Albuquerque, New Mexico, to test Lyft Scooters in their respective cities. Each recognizes that she or he has a 2% chance of experiencing an accident. If an accident occurs, a $12,000 will be lost due to injury and property damage.

For questions 4-11, assume that Zahra and Mateo decide to pool (or share equally) their losses. The losses are uncorrelated.

4. How much will each person need to pay into the pot of pooled money in order to cover their losses in the event they both experience an accident?

5. What is the combined probability distribution when the two loss potentials are pooled?

6. What is the expected total loss for the distribution of pooled losses?

7. What is the expected loss per person from the distribution of pooled losses?

8. What is the standard deviation of the distribution of pooled losses?

9. What is the standard deviation of the distribution of pooled losses, per person?

10. If the number of people in the pool increases from 2 to 1000, how will this change influence each of the following? Use words, not numbers, to state whether they will they increase, decrease or stay the same.
    
    1. The expected total loss
       
       
    2. The expected loss per person
       
       
    3. The standard deviation of the total loss
       
       
    4. The standard deviation of loss per person

Based on your work so far, why might Zahra and Mateo choose to pool their losses?

The following data give the number of hours 5 students spent studying and their corresponding grades on their midterm exams.

Step 1 of 6 : Calculate the sum of squared errors (SSE). Use the values b0=59.2382 and b1=2.8095 for the calculations. Round your answer to three decimal places.

Step 2 of 6: Calculate the estimated variance of errors, s^2e. Round your answer to three decimal places.

Step 3 of 6: Calculate the estimated variance of slope, s^2b1. Round your answer to three decimal places.

Step 4 of 6: Construct the 95% confidence interval for the slope. Round your answers to three decimal places.

Lower and upper endpoints.

Step 5 of 6: Construct the 98% confidence interval for the slope. Round your answers to three decimal places. Lower and upper endpoints

Step 6 of 6: Construct the 90% confidence interval for the slope. Round your answers to three decimal places. Lower and upper endpoints.

A company manufactures light bulbs. These light bulbs have a length of life that is normally distributed with a known standard deviation of 40 hours. If a sample of 36 light bulbs has an average life of 780 hours, find the 95 percent confidence interval for the population mean of all light bulbs manufactured by this company.

Self-efficacy is a general concept that measures how well we think we can control different situations. A multimedia program designed to improve dietary behavior among low-income women was evaluated by comparing women who were randomly assigned to intervention and control groups. Participants were asked, "How sure are you that you can eat foods low in fat over the next month?" The response was measured on a five-point scale with 1 corresponding to "not sure at all" and 5 corresponding to "very sure." Here is a summary of the self-efficacy scores obtained about 2 months after the intervention:

(a) Do you think that these data are Normally distributed? Explain why or why not.

The distribution is not Normal because all scores are integers.

The distribution is Normal because the sample was randomly assigned.    

The distribution is Normal because the sample sizes are large.

The distribution is not Normal because the sample included only women.

The distribution is Normal because the standard deviation is smaller than the mean.

(b) Is it appropriate to use the two-sample t procedures that we studied in this section to analyze these data? Give reasons for your answer.

The t procedures should not be appropriate because we do not have Normally distributed data.

The t procedures should not be appropriate because the sample sizes are not large enough.     

The t procedures should be appropriate because we have Normally distributed data.

The t procedures should be appropriate because we have two large samples with no outliers.

The t procedures should not be appropriate because the two groups are different sizes.

(c) Describe appropriate null and alternative hypotheses.

H₀: μ_Intervention = μ_Control; H_a: μ_Intervention > μ_Control (or μ_Intervention < μ_Control)

H₀: μ_Intervention ≠ μ_Control; H_a: μ_Intervention > μ_Control (or μ_Intervention = μ_Control)

H₀: μ_Intervention = μ_Control; H_a: μ_Intervention < μ_Control (or μ_Intervention ≠ μ_Control)

H₀: μ_Intervention = μ_Control; H_a: μ_Intervention > μ_Control (or μ_Intervention ≠ μ_Control)

H₀: μ_Intervention ≠ μ_Control; H_a: μ_Intervention < μ_Control (or μ_Intervention = μ_Control)

Some people would prefer a two-sided alternative in this situation while others would use a one-sided significance test. Give reasons for each point of view.

The two-sided alternative reflects the researchers' (presumed) belief that the intervention would decrease scores on the test. The one-sided alternative allows for the possibility that the intervention might have had a positive effect.

The two-sided alternative reflects the researchers' (presumed) belief that the intervention would increase scores on the test. The one-sided alternative allows for the possibility that the intervention might have had a negative effect.     

The one-sided alternative reflects the researchers' (presumed) belief that the intervention would increase scores on the test. The two-sided alternative allows for the possibility that the intervention might have had a negative effect.

The one-sided alternative reflects the researchers' (presumed) belief that the intervention would decrease scores on the test. The two-sided alternative allows for the possibility that the intervention might have had a positive effect.

The one-sided alternative reflects the researchers' (presumed) belief that the intervention would decrease scores on the test. The two-sided alternative allows for the possibility that the intervention might have had a negative effect.

(d) Carry out the significance test using a one-sided alternative. Report the test statistic with the degrees of freedom and the P-value. (Use μ_Intervention − μ_Control. Round your test statistic to three decimal places, your degrees of freedom to the nearest whole number, and your P-value to four decimal places.)

Write a short summary of your conclusion.

We reject H₀ and conclude that the intervention increased test scores.

We do not reject H₀ and conclude that the intervention had no significant effect on test scores.     

(e) Find a 95% confidence interval for the difference between the two means. Compare the information given by the interval with the information given by the significance test.

_______, _______

(f) The women in this study were all residents of Durham, North Carolina. To what extent do you think the results can be generalized to other populations?

The results for this sample may not generalize well to other areas of the country.

The results for this sample will generalize well to all other areas of the country.     

The level of calcium in the blood in healthy young adults varies with mean about 9.5 milligrams per deciliter and standard deviation about 0.4. A clinic in rural Guatemala measures the blood calcium level of 160 healthy pregnant women at their first visit for prenatal care. The mean based on this sample is 9.57. Is this an indication that the mean calcium level in the population from which these women come differs from 9.5?

a) Define μ in the context (in words).

b) State H₀ and H_a.

c) Find the z-statistic.

d) Give the P-value.

e) Report your conclusion in context using a significance level of 5%.

f) Give a 95% confidence interval for the mean calcium level μ in this population. Interpret result.

Consider the following time series data.

Quarter Year 1 Year 2 Year 3

1 4 6 7

2 2 3 6

3 3 5 6

4 5 7 8

1.plot with line dot chart.

2.What type of pattern exists in the data?

a.Upward Trend Patter,

b. Downward Trend Pattern

c. Horizontal Pattern With Seasonality.

3.Use a multiple regression model with dummy variables as follows to develop an equation to account for seasonal effects in the data. Qtr1 = 1 if Quarter 1, 0 otherwise; Qtr2 = 1 if Quarter 2, 0 otherwise; Qtr3 = 1 if Quarter 3, 0 otherwise. If required, round your answers to three decimal places. For subtractive or negative numbers use a minus sign even if there is a + sign before the blank. (Example: -300)

a. Value = ( )  + ( ) Qtr1 + ( )  Qtr2 + ( ) Qtr3 +  t

4.Compute the quarterly forecasts for next year. If required, round your answers to two decimal places.

1. Quarter 1 forecast =
2. Quarter 2 forecast =
3. Quarter 3 forecast =
4. Quarter 4 forecast =

As the newly hired manager of a company that provides cell-phone service, you want to determine the proportion of adults in your state that live in a home with a cell phone but no land line service.

1.Assuming you have no prior information, how many people must you survey to ensure that your estimate has no more than a 4% margin of error, with 95% confidence?

(Hint: use p=50% when you haven't done a pilot study)

2.Suppose you do a small pilot study of 25 adults in your state, and find that 5 of those people live in a home with a cell phone but do not have land line service. Using that information, how many people must you survey to ensure that your estimate has no more than a 4% margin of error, with 95% confidence?

In the Star Wars franchise, Yoda stands at only 66cm tall. Suppose you want to see weather or not hobbits from Lord of the Rings are taller than Yoda, on average. Distributions are normally distributed. A sample of 7 hobbits, average height x=80cm and a standard deviation s=10.8 cm. Does sample evidence suggest at the 1% level of significance that the average hobbit is taller than Yoda? Sketch rejection and non-rejection