A professor in the accounting department of a business school claims that there is much more variability in the final exam scores of students taking the introductory accounting course as a requirement than for students taking the course as part of a major in accounting. Random samples of 16 non-accounting majors (group 1) and 15 accounting majors (group 2) are taken from the professor's class roster in his large lecture, and the following results are computed based on the final exam scores:

n₁ = 16, S₁² = 154.6,    n₂ = 15, S₂² = 48.5

(a) At the 0.05 level of significance, is there evidence to support the professor's claim?

(b) What assumptions do you make here about the two populations in order to justify your use of the F test?

A health spa has advertised a weight reducing program and has claimed that the average participant in the program loses at least 20 pounds. A somewhat overweight executive is interested in the program but is skeptical about the claims and asks for some hard evidence. The spa allows him to select randomly the records of ten participants and record their weights before and after the program.

Test whether the average weight loss is at least 20 pounds.

Participant Before After

Ross Erickson 189 170

Josh Way 202 179

Laura Ewok 220 203

Luke Haas 207 192

Brandon Bott 194 172

etc. etc. etc.

State H0 and H1. You MUST show the five-step process for determining H0 and H1. (1 pt.) Be very careful how you handle the 20 pound difference! The variable with the larger numbers MUST be on the left.

A research institute poll asked respondents if they felt vulnerable to identity theft. In the​ poll, n equals 942 and x equals 520 who said​ "yes." Use a 90 % confidence level.

A. Find the best point of estimate of the population of portion p. (Round to three decimal places as​ needed.)

B. Identify the value of the margin of error E. (round to three decimal places as needed)

C. Construct the confidence interval. _ < p <_ round to three decimal places.

D. Write a statement that correctly interprets the confidence interval.

The coins (by magic) always land on the same side (both heads or both tails). Suppose you flip a penny and a dime. Let X be the result of flipping the penny where we assign the value of Heads to be 2 and the value of Tails to be 1, and let Y be the result of flipping the dime where we assign the value of Heads to be 4 and Tails to be 3. (So, for example, X(heads)=2.) Find E[X], E[Y], E[X+Y] andE[XY]. Compute Var(X+Y) and Var(XY).

We see different charts and graphs in our daily lives. How can information and data be presented through different charts and graphs in such a way that the same data is perceived differently based on presentation?

The following data lists the ages of a random selection of actresses when they won an award in the category of Best​ Actress, along with the ages of actors when they won in the category of Best Actor. The ages are matched according to the year that the awards were presented. Complete parts​ (a) and​ (b) below.

Actress (years) 31   25   29   31   35   25   25   42   30   32

Actor (years)    56   40   39   34   29   37   52   35   34   44

a. Use the sample data with a 0.01 significance level to test the claim that for the population of ages of Best Actresses and Best​ Actors, the differences have a mean less than 0​ (indicating that the Best Actresses are generally younger than Best​ Actors).

In this​ example, μd is the mean value of the differences d for the population of all pairs of​ data, where each individual difference d is defined as the​ actress's age minus the​ actor's age. What are the null and alternative hypotheses for the hypothesis​ test?

H0​: μd (1) _____ , _____ years

H1​: μd (2) _____ , _____ years

​(Type integers or decimals. Do not​ round.)

(1) >

<

≠

=

(2) <

=

≠

>

Identify the test statistic.

t= _____ ​(Round to two decimal places as​ needed.)

Identify the​ P-value.

​P-value=_____ ​(Round to three decimal places as​ needed.)

What is the conclusion based on the hypothesis​ test?

Since the​ P-value is (3) _____ the significance​ level, (4) _____ the null hypothesis. There (5)_____ sufficient evidence to support the claim that actresses are generally younger when they won the award than actors.

(3) less than or equal to

greater than

(4) reject

fail to reject

(5) is

is not

b. Construct the confidence interval that could be used for the hypothesis test described in part​ (a). What feature of the confidence interval leads to the same conclusion reached in part​ (a)?

The confidence interval is _____ ​year(s)<μd< _____ ​year(s).

​(Round to one decimal place as​ needed.)

What feature of the confidence interval leads to the same conclusion reached in part​ (a)?

Since the confidence interval contains (6) _____ (7) _____ the null hypothesis.

(6) zero,

only negative numbers,

only positive numbers,

(7) reject

fail to reject

2. A pharmacy is using X bar and R charts to record the time it takes to fill a prescription after the customer has turned in or called in the prescription. Each day, the pharmacy records the times it takes to fill six prescriptions. During a 30-day period, the hospital obtained the following values: X double bar = 20 minutes; R bar = 4 minutes. The upper and lower specifications are 23 minutes and 13 minutes respectively. What is the value of Cp, to two decimal places?

Real Fruit Juice: A 32 ounce can of a popular fruit drink claims to contain 20% real fruit juice. Since this is a 32 ounce can, they are actually claiming that the can contains 6.4 ounces of real fruit juice. The consumer protection agency samples 56 such cans of this fruit drink. Of these, the mean volume of fruit juice is 6.36 with standard deviation of 0.21. Test the claim that the mean amount of real fruit juice in all 32 ounce cans is 6.4 ounces. Test this claim at the 0.05 significance level.

(a) What type of test is this?

This is a two-tailed test.

This is a left-tailed test.    

This is a right-tailed test.

(b) What is the test statistic? Round your answer to 2 decimal places.
t-<sub>x= 2

(c) Use software to get the P-value of the test statistic. Round to 4 decimal places.
P-value = 3

(d) What is the conclusion regarding the null hypothesis?</sub>

reject H₀

fail to reject H₀    

(e) Choose the appropriate concluding statement.

There is enough data to justify rejection of the claim that the mean amount of real fruit juice in all 32 ounce cans is 6.4 ounces.

There is not enough data to justify rejection of the claim that the mean amount of real fruit juice in all 32 ounce cans is 6.4 ounces.

We have proven that the mean amount of real fruit juice in all 32 ounce cans is 6.4 ounces.

We have proven that the mean amount of real fruit juice in all 32 ounce cans is not 6.4 ounces

The Colgate company believes its toothpaste is more effective than its leading rival, Aim, in fighting tooth decay. A small scale clinical trial was held with 25 patients using Colgate and 28 using Aim. The results showed that the average and variance of the number of cavities for Colgate was 10.4 and 12.82, respectively, with the results for Aim being 12.6 and 9.66. It is assumed that the population variances are the same and the distribution of the number of cavities for both groups closely approximates a normal distribution. Use an alpha of 0.01.

1. If the hypotheses are to be written in the form of the average of Aim minus the average of Colgate, what is the direction of the alternative hypothesis used to test Colgate's belief. Type the letters gt (greater than), ge (greater than or equal to), lt (less than), le(less than or equal to) or ne (not equal to) as appropriate in the box.
2. Determine the standard error for the difference between means, reporting your answer to three decimal places.
3. Calculate the test statistic, reporting your answer to two decimal places.
4. Is the null hypothesis rejected for this test? Type yes or no.
5. Regardless of your answer for 4, if the null hypothesis was rejected, can we conclude that Colgate's belief is valid at the 1% level of significance? Type yes or no.

Each of the following statements corresponds (somewhat naturally) to a statistical hypothesis. For each statement, decide

If it involves one or more populations; one or more variables. [No answer needed.]

The population(s) and the variable(s) involved.

The form of the test.

Single parameter

Two parameter or multiple parameter—always the same parameter for multiple populations (or possibly multiple variables)

Single distribution

Two distributions or multiple distributions—either two different variables, or the same variable for multiple populations

Independence

Note with measures of association will have one parameter (g, r, b) with a pair of populations

If the hypothesis is on one or more parameters, give

The parameter(s) involved.

The Null and the Alternate hypotheses. or

Whether the hypothesis test is one or two-sided. or

If the hypothesis is on one or more distributions, give

The Null and the Alternate hypotheses.

Why don’t we need to specify whether one-sided or two-sided?

1.The typical American teenage girl uses her cell phone 27 hours per week.

2.There is a negative association between the severity of a patient’s illness and his/her opinion of food in the hospital.

3.The average Toro Loco bill for a dinner for four is $97.53.

4.The percentage of couples who divorce is higher for those who lived together before marriage than for those who didn’t.

5.70% of all students who need more than three remedial courses in college will not graduate.

What is the point estimate for the population mean?

In your own words, what is the margin of error? Why is it so important for constructing a confidence interval?

Suppose that I construct a confidence interval for the mean test grade on exam 1 using Statcrunch and get Upper Limit, 68.9 and a lower limit 76.3. State the conclusion for the confidence interval.

What happens to the confidence interval as we increase the sample size? Explain your reasoning (explanations without reasoning will not be given credit.)

When should we use the t-distribution instead of the z-distribution?

It has been reported that 45% of all college students use Twitter If we survey a simple
random sample of n = 225 college students and ask if they use Twitter, the percentage who
say “yes” will vary if the sampling method is repeated. In fact, the sampling distribution of
the percentage who say they use Twitter, in many samples of size n = 225, will be Normal in
shape, with mean (or center) of 45% and standard deviation of 3.3%. Based on this
information, we know that the probability of obtaining a sample (of size n = 225) where
39% or fewer students say they use Twitter is

. Suppose that the lifetime of a charged electronic device is uniformly distributed in the interval [5, 6] hours. Suppose you take 20 measurements. Compute the following • The probability that the mean over the 10 measurements exceeds 5.6 hours. • The probability that the mean lies between 5.45, and 5.55 hours. • The probability that the mean exceeds 6.1 hours. Think about this last point carefully: Do it first by applying the central limit theorem, but then explain whether this answer makes sense or not.

6) Provide an example of counting in your everyday life. Think of an example where you could use a counting method and describe the method.