A researcher is interested in whether college students get enough sleep. She suspects
that they get less than 8 hours of sleep on average. The sample mean (x ̄) for 65 students
was 7.08 hours. The standard deviation of number of hours students slept is s=1.8.
(a) Determine the null and alternative hypothesis for the test. What is the parameter
in this study?

(b) The p-value for the test is <0.0001. Using a significance level of .05, write a one or
two sentence conclusion in context of the problem.

(c) Calculate 95% confidence interval for μ, the mean number of hours college students
sleep per night. Interpret the confidence interval. Be sure to use the word mean or average in your interpretation and don’t forget units. If you are doing the calculations by hand use t* = 1.998.

(d) Does your confidence interval support the results of the hypothesis test? Explain.

2. The College Board reported that the mean SAT score in 2009 was 540 for all US High
School students that took the SAT. A teacher believes that the mean score for his
students is greater than 540. He takes a random sample of 50 of his students and
the sample mean score for the 25 students is 565 with a sample standard deviation of
100. Does he have evidence that his students, on average, do better than the national
average?
(a) State the null and alternative hypotheses.

(b) The p-value for the above test was 0.1117. State a conclusion in context of the
problem. Use a significance level of 0.05.

(c) A 95% confidence interval for μ is (523.7,606.3). Interpret the confidence interval
in context of the problem.

(d) Does your confidence interval support the results of the hypothesis test? Explain.

A telemarketer knows that, on average, he is able to make three sales in a 45-minute period. Suppose the number of sales he can make in a given time period is Poisson distributed.

a) What is the probability that he makes two sales in a 30 -minute period?

b )What is the probability that he makes at least two sales in a 30-minute period?

c) What is the probability that he makes only one sale in an hour-long period?

Please provide good explanation.

In September 2000, each student in a random sample of 100 chemistry majors at a large university was asked in how many lab classes he or she was enrolled. The results indicated a mean of 1.65 lab classes and a standard deviation of 1.39. To determine whether the distribution changed over the past 10 years, a similar survey was conducted in September 2010 by selecting a random sample of 100 chemistry majors. The results indicated a sample mean of 1.82 and a standard deviation of 1.51. Do the data provide evidence that the mean number of lab classes taken by chemistry majors in September 2000 is different from the mean number of lab classes taken in 2010? Perform an appropriate statistical test using α = 0.02. (10 points)SHOW ALL WORK.

IQ tests are designed to yield results that are approximately Normally distributed. Researchers think believe that the standard deviation, σ, is 15. A reporter is interested in estimating the average IQ of employees in a large high-tech firm in California. She gathers the IQ information on 22 employees of this firm and recoreds the sample mean IQ as 106. Let X represent a random variable describing a person's IQ: X~N(µ, 15).

a. Find the standard error of the sample mean.

b. Calculate a 90% confidence interval.

c. Interpret the confidence interval in the context of the problem.

( Need excel form )

Scenario:

1. On March 28 at 1:30 pm, I randomly selected 10 states and found the number of coronavirus cases in each of them.  This gave me an average of 939 cases with a standard deviation of 1543.  Assume the number of cases in each state is normally distributed.  Create a 90% confidence interval for the actual number of coronavirus cases in each state.

Question:

3. Using the scenario from question 1, how many states would need to be selected to be 90% confident that the sample mean number of cases would be within 500 of the actual mean?

Iconic memory is a type of memory that holds visual information for about half a second (0.5 seconds). To demonstrate this type of memory, participants were shown three rows of four letters for 50 milliseconds. They were then asked to recall as many letters as possible, with a 0-, 0.5-, or 1.0-second delay before responding. Researchers hypothesized that longer delays would result in poorer recall. The number of letters correctly recalled is given in the table.

(a) Complete the F-table. (Round your values for MS and F to two decimal places.)

(b) Compute Tukey's HSD post hoc test and interpret the results. (Assume alpha equal to 0.05. Round your answer to two decimal places.)

The critical value is _____ for each pairwise comparison.

Which of the comparisons had significant differences? (Select all that apply.)

a) The null hypothesis of no difference should be retained because none of the pairwise comparisons demonstrate a significant difference.

b) Recall following a half second delay was significantly different from recall following a one second delay.

c) Recall following no delay was significantly different from recall following a half second delay.

d) Recall following no delay was significantly different from recall following a one second delay.

The director of research and development is testing a new medicine. She wants to know if there is evidence at the 0.01 level that the medicine relieves pain in more than 313 seconds. For a sample of 34 patients, the mean time in which the medicine relieved pain was 320 seconds. Assume the standard deviation is known to be 24.

Step 1 of 5: Enter the hypotheses:

Step 2 of 5: Enter the value of the z test statistic. Round your answer to two decimal places.

Step 3 of 5: Specify if the test is one-tailed or two-tailed.

Step 4 of 5: Enter the decision rule.

Step 5 of 5: Enter the conclusion.

Major health studies try very hard to select a sample that is representative of the various ethnic groups making up the U.S. population. Here is the breakdown, by ethnicity, of subjects enrolled in a major study of sleep apnea:

The known ethnic distribution in the United States, according to census data, is as follows:

a. We want to know if the data from the sleep apnea study support the claim that the ethnicity of the subjects fits the ethnic composition of the U.S. population. What does the null hypothesis for this test state?

1. All five counts are equal.
2. All five sample proportions are equal.
3. All five population proportions are equal.
4. All five population proportions are equal to their respective U.S. census proportions.

b. What is the expected count of Hispanics under the null hypothesis (show calculation)?

a. 277

b. 25.207

c. 572.754

d. 152.72

c. At significance level alpha = 1%, what should you conclude

1. a. composition of the U.S. population.
2. b. The data are consistent with a uniform distribution of ethnicities.
3. c. The data prove that the population studied matches the ethnic composition of the U.S. population.
4. e. We are unable to conclude anything because the test assumptions are not met.

1. A sociologist studied random samples of full-time employees in a particular occupation – six women and six men – to determine whether gender has an influence on the average (mean) number of hours worked per day. She obtained the following results:

           Women                Men  

                10                      12

                 9                        9

                 7                        8

                 4                       10

                 9                       11

                 6                        7     

Use a .01 alpha level to test whether there is a gender difference in the mean number of hours worked, and answer the following questions:

1. Is this a one-tailed or two tailed test? How do you know?
2. What is the critical value of the test statistic?
3. What is the obtained value of the test statistic?
4. What decision about the null hypothesis does your test lead to?
5. What does this indicate about gender differences in hours worked among the population working in this occupation?
6. Would your decision be different if you used an alpha level of .05? Explain.

Find the following

5C1

7P0

10C2

8P3

1. Theater tickets for a hit show have four prices depending on seating. The prices ae $50, $100, $150 and $200. The probability a ticket sells for $50 is .4. The probability it sells for $100 is .15. The probability it sells for $150 is .2.

1. Find the probability a ticket sells for $200.

2. Find the expected cost (mean cost) of a ticket.

3. Find the standard deviation for the cost of a ticket

4. Find the variance for the cost of a ticket

2. A person pays $2.00 to play the following carnival game: A die is rolled one time. If an even number comes up the person pays an additional $2.50. If it comes up odd, the player receives a payment of $5.00 and gets the $2.00 back. Find the players expected profit if (s)he plays this game.

3. Sixty percent of all shoppers in a given shopping center use credit cards for their purchases. If 20 shoppers make purchases, find the probability that:

1. exactly 12 use credit cards.

2. exactly 7 do not use credit cards.

3. At most 10 use credit cards

4. More than 13 use credit cards

4. The probability a person passes the Bar exam is .46. If 290 people in this city take the exam:

1. Find the mean number who pass.

2. Find the standard deviation for the number who pass.

5. Find each of the following probabilities for a value chosen at random from a Standard Normal (Z) distribution.

1. the probability the value is more than 2.7

2. the probability the value is between –2.01 and 2.21

3. The probability the value is less than –3.2

6. The hourly wage for workers in a fast food restaurant is Normally distributed with a mean of $5.85 and a standard deviation of $0.35. If a worker is selected at random, find the probability that:

1. (S)he earns less than $5.50 an hour

2. (S)he earns between $5.90 and $6.40 an hour.

3. (S)he earns at least $6.00 an hour

7. The mean cost of living for a family of four in cities across the country is $65,351 with a standard deviation of $7712. A company is thinking of relocating to a city with a cost of living that is in the bottom 40% of all the cities. Assuming that the distribution is Normally distributed, what is the cutoff score for a city that would make it eligible for consideration by this company?

8. 45% of people have type O blood . If 400 volunteers show up to donate blo, use the Normal approximation to the binomial to find the probability that more than 175 but at most 182 have type O blood.

9. The mean annual rainfall in a particular region is 80 inches with a standard deviation of 8 inches. If a sample of 32 years is selected, what is the probability that the mean annual rainfall for this sample will be less than 79 inches?

It is generally believed that there is a relationship between a college’s acceptance rate and its graduation rate. I wanted to know how strong this relationship is within the top universities in the country so I collected the graduation rate and acceptance rate data of a randomly selected sample of universities from all the top U.S. universities (with an acceptance rate at or below 30%).

b. Calculate the mean and standard deviation for the two variables separately. (4 points total: 1 point for each mean and 1 point for each SD, deduct .5 if an answer is in correct but the calculation process was correct)

Acceptance rate:

Mean = 18

SD = 7.3

Grad Rate

Mean = 90

SD = 5.06

c. Calculate the Z scores for all the scores of the two variables, separately. Tips: It may help to prevent error and to increase clarity if the process and/or the answers (z scores) are listed in a table format.

(2 points total: 1 for Z scores for each variable)

d. Calculate Pearson’s correlation coefficient r. (2 points total: 1 if the process is correct but the answer is wrong)

e. Explain the direction and strength of the relationship based on the r. (1 point total: .5 for strength, .5 for direction)

f. What is the proportion of variance shared between the two variables? (That is, how much of the variance in one variable can be predicted by the variance in the other variable?) (1 point total: -.5 if the process is correct but the answer is wrong)

g. If the researcher wants to perform a two-tailed hypothesis test using this data set so that she can generalize the relationship between the two variables from the sample to the population, what would be the null and alternative hypothesis? Write the hypotheses in words and in symbol notation. (2 points total: 1 for each hypothesis, .5 for written, .5 for symbol notation)

h. Using SPSS to analyze the same dataset yields a p value of .001. Based on α = .05, what would be the conclusion of the hypothesis test (use wording of “reject the null hypothesis” or “fail to reject the null hypothesis”? How do you know? (1 point total: .5 for conclusion, .5 for rationale)

Given the following sample observations, draw a scatter diagram on a separate piece of paper.

1. Compute the correlation coefficient. (Round your answer to 3 decimal places.)

Coefficient of correlation ________

2. Does the relationship between the variables appear to be linear?

• Yes

• No

3. Try squaring the x variable and then determine the correlation coefficient. (Round your answer to 3 decimal places.)

Coefficient of correlation ______

A survey of 200 drivers who were at fault in an accident found that 62% were dropped by their insurance carrier. Conduct a hypothesis test at a 0.10 level of significance to determine if the percentage of drivers dropped by the insurance carrier is different than 60%. State the null and alternate hypotheses. Use whichever applicable approach to hypothesis testing that you prefer, specify the numerical comparisons to be made, and state your conclusion.

according to a study by the american pet food dealers association 63% of U>S> households own pets. A report is being prepared for an editorial in the san Francisco chronicle to study pet ownership in San Francisco. As a part of the editorial a random sample of 300 households in San Francisco showed 202 own pets. Cn we conclude that more than 63 percent of the population San Francisco own pets? use a .10 significance level