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Whenever we perform a statistical test, we calculate a so-called p-value, which ranges between 0.00 and 1.00. In general terms, the value of p tells us the probability of drawing a sample WITH THESE CHARACTERISTICS if the null hypothesis is TRUE.

Here's a simple example.
H1: On average, ten-year-old boys are taller than ten-year-old girls.
H0: On average, ten-year-old boys and girls are the same height.

Suppose we sample five boys and five girls, and find that the average height of the boys is 0.5 inches more than the average height of the girls. The value of p would be close to 1, because it's very likely that we could have randomly drawn a sample with such a difference, even if the overall average height of boys and girls is actually the same.

We do the test again, but this time we take a sample of 500 boys and 500 girls. On average, the boys are 0.5 inches taller. In this case, the value of p would be close to zero, because the chance of finding this difference in such a large sample is remote if there's actually NO difference. Think about this, and make sure you understand it.

Before doing our test, we set a level of significance (LOS), which is a value of p. If the LOS is less than a certain value, we'll reject the null hypothesis -- otherwise, we'll not reject it. The LOS is usually set at 0.05; but is that always necessary?

Suppose I'm tasked to evaluate a new textbook. One group of 50 students uses the new book, another group of 50 stays with the old book. On the final exam, the students who used the new book score, on average, 1 point higher (p = 0.23). Other information: both books are in stock in the university bookstore, the prices are roughly the same, and faculty members have no particular preference for one book over the other. Should I recommend the new book be adopted? Why or why not?

#### Solution Preview

In general terms, the value of p of 0.23 tells us the probability of drawing a sample of 100 students and half get a better grade with the new book is 23% and the following null hypothesis is TRUE.

H1: The new book is stastically better than the old book for students' grades.
H0: The new book is stastically no better than the old book for students' grades.

23% is too high to recommend the book, in a very strict sense. The difference in student's grades could be due to other reasons, like study habits, etc. We could say there is not enough data to reject the old book in favor of the new. A wider sample of more students, or a better test to get a more ...

#### Solution Summary

Detailed example of the rationale to accept, or to reject based on this specific example.

\$2.19

## Business Statistics (3 Part Questions)

Writing Hypotheses

Read the situation. Then write the hypotheses in correct mathematical notation. Do not conduct any statistical tests. Just write the hypotheses. Insert your answers between the problems.

Here are some things to keep in mind:

1) On the Hypothesis Testing Worksheet, all you need to do is write the null and alternative hypotheses for each situation.

2) The null hypothesis will always be "=".

3) You can use either "≠" or "not =" for "does not equal". Greater than and less than is ">" or "<", respectively.

4) The alternative hypothesis wil be "not =" (2 tailed test) of ">" or "<" (one tailed test).

5) When determining what the null and alternative hypotheses are, realize that the alternative is the new information, what you are trying to prove. The null is what has been believed to be true up until now.

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1) A bowler who has averaged 196 pins in the past year is asked to experiment with a ball made of a new kind of material. He rolls several games with the new ball. Has the new ball improved his game?

2) An advertisement claims that chewing NoCav gum reduces cavities. To test the claim, you conduct a study in which participants who chew the gum are compared to the national average of 3 cavities found per year.

3) In a speech to the Chamber of Commerce, a city councilman claims that in his city less than 15% of the adult male population are unemployed. An opponent in the upcoming election wants to test the councilman's claim.

4) The councilman is starting to get worried about the upcoming election. He has enjoyed 63% support for several years, but the political climate has been changing. He wants to know if his support has changed.

5) A production process is considered to be under control if the machine parts it makes have a mean length of 35.50 mm with a standard deviation of 0.45 mm. Whether or not the process is under control is decided each morning by a quality control engineer who bases his decision on a random sample of size 36. Should he ask for an adjustment of the machine on a day when he obtains a mean of 35.62 mm?

6) Jim, the owner of Jim's Grocery, knows that Plain Chips have always outsold Spicy chips. However, sales of Spicy chips have been increasing. Jim wants to determine if the average weekly sales of Spicy chips have indeed surpassed that of Plain chips.

7) Jim now wants to know if Plain and Spicy chips have the same percentage of defective product (i.e. underfilled bags, torn bags, wrong flavor in the bags, etc.).

8) The Great Vehicle Co. just introduced New SUV, claiming it can pull more weight than Old SUV. After testing 150 vehicles of each model, Old SUV had a mean pull weight of 5032 pounds with a standard deviation of 72 pounds. New SUV had a mean pull weight of 5462 pounds with a standard deviation of 154 pounds. Is the claim valid at a .05 level of significance?

9) The Great Vehicle Co. has a competitor, Amazing Autos, that claims people who purchase its competing vehicle, the Sport Off Road Vehicle (SORV), have higher customer satisfaction than New SUV. Out of 736 people who purchased the SORV last month, 534 said they were satisfied. Out of 521 people who purchased New SUV last month, 375 said they were satisfied. Is there a higher percentage of people who are satisfied with the SORV than with New SUV?

10) The Great Vehicle Company wants to counter Amazing Autos's claim by making its own claim that New SUV has a lower percentage of defective vehicles. The research team tested 536 vehicles of each model and found that SORV had 53 defective units, while New SUV had only 51 defective units.

Statistics Problems

1) Ask 10 people (get 5 males and 5 females) the following questions

A) Their ages

B) How many vitamins they take daily

C) How many carbonated sodas they drink each day

D) How many alcoholic beverages they drink per month

E) Write your own question. Ask your participants if they agree with something or if they do something. For example, you may want to ask them if they eat popcorn when they go to the movies or if they support a political issue. It must be a yes/no question.

SHOW & SAVE YOUR DATA - You will use the data you gathered above for the problems below

Practice Problems:

1) Use your data from above. This week assume that historically the average person takes 3 vitamins on a daily basis. Conduct a hypothesis test analysis to determine if 3 is still the correct average number. Write your hypotheses in correct statistical notation. Finally use the important numbers from your output to explain your results. Use alpha = 0.05. Post only the relevant numbers, not all of the output; then explain your results.

2) Use your data from above. Analyze if more than 58% support an issue or partake in an activity. (Question E above). Write the hypotheses. Show the relevant numbers. Then explain your results. Use alpha = 0.05.

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