Kolbe, product manager for a line of shoes, is wondering whether to introduce his product line into a new market area. A recent survey of a random sample of 500 households in that market showed a mean household income of $34,000 with a standard deviation of $2,000. On the basis of past experience and of comprehensive studies in current market areas, Kolbe believes the product line will be profitable only in markets where the mean household income (across all households) is greater than $30,000. Should Kolbe introduce the product line into the new market?

Respond to the following in a minimum of 175 words:

This week, we consider how to conduct hypotheses test on one sample data. Discuss the concepts associated with these tests. Consider the following:

The difference between a one tail and a two tailed test.

The importance of stating the null and alternative hypotheses before conducting the test.

The importance of a type one error (p) in conducting the test  

The relationship between the p value and our decision to accept or reject the null hypothesis

Suppose that an airline knows that there is a 95% chance that a passenger for a commuter flight that will hold 189 passengers will show up, and assumes that passengers arrive independently of one another. The airline decides to sell 199 tickets in order to reduce the number of empty seats, expecting 5% of the passengers not to show up.Let X be a random variable that represents the number of people who show up for the flight. Let Y = X –189 be a random variable representing the difference between the number of passengers who show up and the number of seats on the plane.a. Calculate E(X), Var(X), E(Y), and Var(Y).Justify your calculations by stating the type of distribution for X and Y. b.Calculate P(Y > 0). How do you feel about the airline’s decision to sell 199 tickets? c.The airline is conducting a review of their policies. They do not want the bad public relations that go along with having passengers with tickets not getting a seat. They have decided to hire you as a consultant to help give them advice. After some investigating, you have determined that as long as they have enough seats for passengers with tickets 98% of the time, they are willing to accept the risk.What is the largest value of n so that P(Y > 0) ≤0.02?

A Relaxin receptor agonist drug (RRA01) for the acute heart failure treatment is developed by the Sunny Pharmaceutical Company. It is a publicly traded company. The reduction of cardiovascular death (mortality) was used as the end point (results of the research) for this investigation. The null hypothesis is “there is no difference in the cardiovascular mortality reduction between patients who received RRA01 (treatment group) and those who did not receive RRA01 (control group). Discuss the impact (on the company and/or on the patients) of the following two possible clinical trial results to the Sunny Pharmaceutical Company, staff of the company, and the patients. 1. p = 0.002 as the hypothesis test results 2. p = 0.3 as the hypothesis test results.

A property and casualty insurance company (which provides fire coverage for dwellings) felt that the mean distance from a home to the nearest fire department in rural Alabama was at least 10 miles. It set its fire insurance rates accordingly. Members of the community set out to show that the mean distance was less than 10 miles due to the increased number of volunteer fire departments. This, they felt, would convince the insurance company to lower its rates. They randomly identify 64 homes and measure the distance to the nearest fire department for each. The resulting sample mean was 8.7 miles. If σ = 3.5 miles, does the sample show sufficient evidence to support the community’s claim? Use the four step process for Hypothesis Testing.

Step 1 – State Hypothesis in context of the problem.

Step 2 – Gather data, check assumptions, and find rejection region using α.

Step 3 – Calculate the appropriate test statistic and p-value.

Step 4 – State conclusion in context of the problem.

If you were given a large data set, such as the sales over the last year of our top 100 customers, what might you be able to do with these data? What might be the benefits of describing the data?

Describe and differentiate between internal and external threats to validity in an experimental design. Recommend at least one action that you or any researcher can take in response to both internal and external validity threats.

Ms.Watts is a fan of college football, and is a little bummed the Texas Longhorns haven’t been doing as well these past few years. She has a hunch that because The Longhorns are in the highest collegiate athletic division (Division-I), her team is more likely to play a mismatched opponent. That is, The Longhorns are more likely to play games with different point spreads (winning team’s score minus losing team’s score) compared to other Divisions. To test this idea, she looked at a sample of 4 games from a lower division (Division-II) to see if the mean point spread was different compared to The Longhorns’ Division-I group. Overall, Division-I teams had a mean spread of 16.189 points with a standard deviation of 12.128 points.

1. The results of the four Division-II games from Ms. Watt's sample are below. Calculate the mean point spread for this sample.

2. Calculate the standard error.

3. State the null hypothesis based on what Ms.Watts believes about mean point spreads in Division-I compared to Division-II football games.

4. State the research hypothesis based on what Ms.Watts believes about mean point spreads in Division-I compared to Division-II football games.

5. Calculate the z-statistic to test the hypothesis you formulated in Questions 3 & 4 using the mean point spread for Division I as the comparison population to the mean point spread you calculated for #1.

6. Given the convention of p<.05, what can you conclude about the mean point spread found in Division-II compared to the mean point spread in Division-I teams? First, make a decision regarding your hypothesis, then state your conclusion.

The USA has been invaded by a ship of 6 aliens -- well, sort of, they actually just flew here from planet YB54D (known to them simply as "Home") as a part of their search for extraterrestrial life. Our military contained them immediately and we are holding them captive for further study (from this sample of 6 aliens we hope to be able to predict what the rest of their kind -- i.e., their entire population -- will be like). One of the first things we want to assess is their hostility; thus, we send in a psychologist who administers the Buss-Perry Aggression Questionnaire (BPAQ), which rates hostility on a scale of 8 to 40, with higher ratings indicating higher hostility. Their scores are as follows:

Alien 1: 20   Alien 4: 9

Alien 2: 17 Alien 5: 13  

Alien 3: 31 Alien 4: 38  

What would the BPAQ score be of an alien who is 1.5 standard deviations below the mean (round to two decimal places)?

What would the BPAQ score be of an alien who is 1 standard deviation above the mean (round to two decimals)?

1. Dihybrid crosses involving plants with either white or yellow flower and either tall or short morphs were done. The yellow allele is dominant over the white allele, and the tall allele is dominant over the short allele. The following are the observed numbers of each combination. Do these data fit the expected distribution?

a. what kind of statistical test needs to be performed?

b. Will you need to test for equal variance? If so, what are your results and how does that influence the next steps in your analysis?

c.What are your null and alternative hypotheses?

H0:

HA:

d. Discuss the results of your analysis. Will you accept or reject your null hypothesis? Why? What can you specifically say about the data?

In the EAI sampling problem, the population mean is $51,900 and the population standard deviation is $4,000. When the sample size is n = 30, there is a 0.5887 probability of obtaining a sample mean within +/- $600 of the population mean. Use z-table.

What is the probability that the sample mean is within $600 of the population mean if a sample of size 60 is used (to 4 decimals)?

What is the probability that the sample mean is within $600 of the population mean if a sample of size 120 is used (to 4 decimals)?

The Acme Company manufactures widgets. The distribution of widget weights is bell-shaped. The widget weights have a mean of 49 ounces and a standard deviation of 7 ounces. Use the Empirical Rule and a sketch of the normal distribution in order to answer these questions.

a) 68% of the widget weights lie between ___ and ____

b) What percentage of the widget weights lie between 28 and 56 ounces?  %

c) What percentage of the widget weights lie above 35 ?  %

A sociologist surveys 50 randomly selected citizens in each of two countries to compare the mean number of hours of volunteer work done by adults in each. Among the 50 inhabitants of Lilliput, the mean hours of volunteer work per year was 52, with standard deviation 11.8. Among the 50 inhabitants of Blefuscu, the mean number of hours of volunteer work per year was 37, with standard deviation 7.2.

1. Construct the 99% confidence interval for the difference in mean number of hours volunteered by all residents of Lilliput and the mean number of hours volunteered by all residents of Blefuscu.

2. Test, at the 1% level of significance, the claim that the mean number of hours volunteered by all residents of Lilliput is more than ten hours greater than the mean number of hours volunteered by all residents of Blefuscu.

3. Compute the observed significance of the test in part (b).

What are the criteria used for evaluating a discrimination funtion? define them.