A credit union is evaluating their staffing schedule to assure they have sufficient staff for their drive-up window during the lunch hour (12:00 pm to 1:00 pm). Assume the number of people who arrive at their drive-up window in a 15-minute time period during the lunch hour has a Poisson distribution with λ = 2.6.

a. What is the probability no customers will arrive between 12:15 and 12:30?

b. What is the probability fewer than 2 people will arrive between 12:15 and 12:45?

A professor wears for each class a combination of : one of his three hats (red, blue, green); one of his pants (black, blue, white, green); one of his shirts (white, red, black); and one of his pair of shoes (black, red, blue, white). He never wears combinations with three items of the same color.

i. How many different combinations are wearable?

ii. The professor is teaching 70 lectures for the term. Can he wear a different combination for each lecture during one term?

iii. If he does wear a different combination each lecture, prove that he must use either the red or the blue shoes that term.

iv. There are 4 terms for the year. Prove that at least one combination will be used at least 3 times during the year.

v. How many valid combinations have blue hat or shoes ?

U.S. consumers are increasingly viewing debit cards as a convenient substitute for cash and checks. The average amount spent annually on a debit card is $7,040 (Kiplinger’s, August 2007). Assume that the average amount spent on a debit card is normally distributed with a standard deviation of $500. [You may find it useful to reference the z table.]

a. A consumer advocate comments that the majority of consumers spend over $8,000 on a debit card. Find a flaw in this statement. (Round "z"value to 2 decimal places and final answer to 4 decimal places.)

b. Compute the 25th percentile of the amount spent on a debit card. (Round "z" value to 3 decimal places and final answer to 1 decimal place.)

for part b I got 6703 but it says it is wrong?

c. Compute the 75th percentile of the amount spent on a debit card. (Round "z" value to 3 decimal places and final answer to 1 decimal place.)

d. What is the interquartile range of this distribution? (Round "z" value to 3 decimal places and final answer to 1 decimal place.)

1. a) Suppose average monthly sales for retail locations across the United States are approximately normally distributed with variance σ^2= 5200. We took a sample of size 50 and found ̄x= 12018,  Using this, conduct a hypothesis test with α= 0.05 to test the null hypothesis that the mean is 12000 vs. the alternative hypothesis that it is not. For full credit, state the null and alternative hypothesis, the test statistic, the rejection region, and your conclusion.

b)Using the setup from part a, if we know that the true mean is 12030, what is the probability of a type II error?

c)Using the setup from part a, what would be the p-value of this test? Would you reject the null hypothesis if α= 0.01? How about if α= 0.1

d)Using the set up from part a, perform the hypothesis test again, but now use the alternative hypothesis that the mean is actually greater than 12000.

e)Using the setup from part a, if we know the true mean is 12030 and we want the probability of a type I error to be 0.05 and the probability of a type II error

to be 0.10, what is the minimum sample size required to ensure this?

Is college worth it? Among a simple random sample of 348 American adults who do not have a four-year college degree and are not currently enrolled in school, 157 said they decided not to go to college because they could not afford school.

1. Calculate a 90% confidence interval for the proportion of Americans who decide to not go to college because they cannot afford it, and interpret the interval in context. Round to 4 decimal places.

( ,  )

2. Suppose we wanted the margin of error for the 90% confidence level to be about 2.25%. What is the smallest sample size we could take to achieve this? Note: For consistency's sake, round your z* value to 3 decimal places before calculating the necessary sample size.

Choose n =

The Civil War. Suppose a national survey conducted among a simple random sample of 1549 American adults, 802 indicate that they think the Civil War is still relevant to American politics and political life.

NOTE: While performing the calculations, do not used rounded values. For instance, when calculating a p-value from a test statistic, do not use a rounded value of the test statistic to calculate the p-value. Preserve all the decimal places at each step.

Enter at least 4 decimal places for each answer in WeBWorK.

1. What are the correct hypotheses for conducting a hypothesis test to determine if the majority (more than 50%) of Americans think the Civil War is still relevant.

A. ?0:?=0.5H0:p=0.5, ??:?>0.5HA:p>0.5
B. ?0:?=0.5H0:p=0.5, ??:?<0.5HA:p<0.5
C. ?0:?=0.5H0:p=0.5, ??:?≠0.5HA:p≠0.5

2. Calculate the test statistic for this hypothesis test.  ? z t X^2 F  =

3. Calculate the p-value for this hypothesis test.

4. Based on the p-value, we have:
A. some evidence
B. extremely strong evidence
C. little evidence
D. strong evidence
E. very strong evidence
that the null model is not a good fit for our observed data.

Is college worth it? Among a simple random sample of 331 American adults who do not have a four-year college degree and are not currently enrolled in school, 131 said they decided not to go to college because they could not afford school.

NOTE: While performing the calculations, do not used rounded values. For instance, when calculating a p-value from a test statistic, do not use a rounded value of the test statistic to calculate the p-value. Preserve all the decimal places at each step.

Enter at least 4 decimal places for each answer in WeBWorK.

1. A newspaper article states that only a minority of the Americans who decide not to go to college do so because they cannot afford it and uses the point estimate from this survey as evidence. What are the correct hypotheses for conducting a hypothesis test to determine if these data provide strong evidence supporting this statement?

A. ?0:?=0.5H0:p=0.5, ??:?>0.5HA:p>0.5
B. ?0:?=0.5H0:p=0.5, ??:?<0.5HA:p<0.5
C. ?0:?=0.5H0:p=0.5, ??:?≠0.5HA:p≠0.5

2. Calculate the test statistic for this hypothesis test.  ? z t X^2 F  =

3. Calculate the p-value for this hypothesis test.

4. Based on the p-value, we have:
A. some evidence
B. extremely strong evidence
C. little evidence
D. very strong evidence
E. strong evidence
that the null model is not a good fit for our observed data.

4. We would prefer to estimate the number of books in a college library without counting them. Data are collected from colleges across Books (in millions)

Using Stepwise regression, show how each of the three factors affects the number of volumes in a college library.

Create one 90%, one 95%, and one 99.7% confidence interval for the question:

Last night did you get at least 8 hours of sleep?

Yes: 11

No: 48

Total: 59

1. Describe the difference between inferential and descriptive statistics.

2. Why don’t we just measure populations? Why do we use samples to infer about populations?

3. Ten people were asked how many siblings they have. Below is the data:

2, 4, 1, 2, 1, 3, 5, 0, 1, 3, 0

4. Create a frequency distribution table.

5. Add on a cumulative frequency column and compute the cumulative frequencies.

6. Add on a relative frequency column and compute the relative frequencies.

The following frequency table summarizes the distances in miles of 100 patients from a regional hospital.

Distance Frequency

0-4 20

4-8 25

4-12 30

12-16 20

16-24 5

Calculate the sample variance and standard deviation for this data (since it is a case of grouped data- use group or class midpoints in the formula in place of X values, and first calculate the sample mean)

Mean cholesterol level of the general population is known to be µ₀ = 175 with a known standard deviation σ = 40. Assume that n = 36 smokers were randomly selected and their cholesterol levels were recorded as x₁, . . . , x₂₅. It is speculated that mean cholesterol level of smokers (denoted by µ) may be different from µ₀ = 175.

1. 1. In testing H₀ : µ = 175 vs. H_A : µ /= 175 at the α = 0.05 level, you will reject H₀ either when x¯ < A or when x¯ > B. Calculate the values of A and B.
2. 2. The researcher is particularly interested in the possibility that the mean cholesterol level of smokers is µ₁ = 182. Thus, determination of the power of a z-test with this particular alternative (µ = µ₁ = 182) in mind is desirable. Which of the above two numbers (A and B) is the most relevant to calculating the power of the z test. Explain your choice both verbally and graphically.
   3. Compute the power of the above z test.

21.HE.B: Captopril is a drug designed to lower systolic blood pressure. When subjects were treated with this drug, their systolic blood pressure readings (in mm Hg) were measured before and after the drug was taken. The results are in the accompanying table on the next page.

(a)      Go through “The Drill” for paired t-tests (Use a 0.05 α-level and the corresponding confidence interval.)

          The Drill:

• Assumptions and Conditions
  • Paired Data Condition

The data must be paired. Only use pairing if there is a natural matching. The two-sample t-test and the paired t-test are not interchangeable.

Independence Assumption

For paired data, the groups are never independent. Need differences independent, not individuals Randomization ensures independence.

Normal Population Assumption

Need to assume the differences follow a Normal model.

• One or two-sided?
• α-level = 0.05
• Statement of the Hypothesis
• Distribution of the sample mean under Ho.
• Make a picture
• Mechanics – test statistic
• p-value
• Interpretation in context
• Conclusion
• Type I and Type II error

(b)      What p-value do we get if we choose the (incorrect) two-sample test of Chapter 20 instead of the (correct) paired t-test? Will it affect the conclusion?

The gynecology unit of a major hospital in Houston conducted a clinical trial to assess a new drug for preventing low birth weight. Nine pregnant women were randomly chosen to receive the drug and 11 others were randomly chosen to receive a placebo during the 25th week of pregnancy. The 20 birth weights are tabulated below.

Patient ID                        Body weight (lb)

Let µ_dand µ_pbe the mean birth weight for the drug and placebo group, respectively. Perform an appropriate test for H₀ : µ_d= µ_pvs. H_A: µ_d /= µ_pat the 5% level. Please articulate the df and the critical value in your analysis.

Test the indicated claim about the means of two populations. Assume that the two samples are independent simple random samples selected from normally distributed populations. Do not assume that the population standard deviations are equal. Use the traditional method or P-value method as indicated. 9) A researcher was interested in comparing the salaries of female and male employees at a particular company. Independent simple random samples of 8 female employees and 15 male employees yielded the following weekly salaries (in dollars).

Female: 495, 760, 556, 904, 520, 1005, 743, 660

Male: 722, 562, 800, 520, 500, 1250, 750, 1640, 518, 904,1150,805,480,970, 605

Use a 0.05 significance level to test the claim that the mean salary of female employees is less than the mean salary of male employees. Use the traditional method of hypothesis testing.