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Hypothesis testing, scatter diagrams, test statistics

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1. The manager of the BiLo Supermarket in Mt. Pleasant, Rhode Island, sampled the following information on the number of times a customer visits the store during a month. The responses of 51 customers were. If EXCEL is used, please import the information into this test document, do not submit separate spreadsheets.

5 2 11 6
1 6 6 3
8 9 5 6
1 4 3 6
3 4 4 4
14 5 6 5
4 2 12 7
10 4 2 5
3 4 3 14
1 9 4 1
7 12 6 6
8 5 5 1
1 4 7

a. Organize the data into a frequency distribution table using 7 classes and create a relative frequency bar chart.

Perform a hypothesis test to see if this sample indicates that the average customer visits the supermarket more than 4 times per week. Test at the level of α= 0.05.

b. State the null and alternative hypotheses
c. State the critical value
d. State the test statistic
e. Interpret the results

2. The manufacturer of "Cardio Glide" exercise equipment wants to study the relationship between the number of months since the glide was purchased and the length of time the equipment was used last week. The data is as follows:

Person Months Owned Hours Exercised
Rupple 12 4
Hall 2 10
Bennett 6 8
Longnecker 9 5
Phillips 7 5
Massa 2 8
Sass 8 3
Karl 4 8
Malrooney 10 2
Veights 5 5

a. Draw a scatter diagram with the "Months Owned" as the independent variable.
b. Compute the coefficient of correlation.
c. Determine the linear regression equation.
d. Test to see if there is a significant relationship between the Months Owned and Hours Exercised at the 95% confidence level.

1) State the null and alternative hypothesis statements.
2) Determine the critical value.
3) What is the test statistic?
4) Interpret the results

e. What percent of the change in the Hours Exercised is "explained" by a change in the Months Owned?
f. Estimate the Hours Exercised of a machine that has been owned for 3 months.
g. Determine a 95% prediction interval for the Hours Exercised of machines that have been owned for 3 months.

3. A baseball card manufacturer plans to re-release some cards of former players. In an effort to determine the demand level for the cards of different players they set up a booth at a card show and at the end of the day had sold a total of 120 of the cards. The number of cards sold for each old-timer is shown below. Can the card manufacturer conclude that there is a preference for the cards of the different players? Use α =0.01.

Player Cards Sold
Tom Seaver 13
Nolan Ryan 33
Ty Cobb 14
George Brett 7
Hank Aaron 36
Johnny Bench 17
Total 120

a. State the null and alternative hypotheses
b. State the critical value
c. State the test statistic
d. Interpret the results

4. A lawn mower manufacturer is studying new methods for mounting the engines on the lawn mower frames. A time and motion study was conducted on two proposed methods to see if there was a difference between the times required to mount the engines for each of the methods. Using an α = 0.10 can it be concluded that one of the two methods requires less time?

Method 1
(minutes) Method 2
(minutes)
2 3
4 7
9 5
3 8
2 4
3

a. State the Null and Alternative Hypotheses.
b. Determine the critical value.
c. Determine the test statistic.
d. Summarize your results.

5. 40% of all books in publication in the US are printed outside of the country. For a random sample of 7 books in the US what is the probability that 2 or more were printed outside the US?

6. The amounts of money requested on home loan applications at Down River Federal Savings follow the normal distribution, with a mean of $110,000 and a standard deviation of $15,000. A loan application is received this morning, what is the probability that the amount requested is between $100,000 and $125,000?

7. A local Ford dealership classifies its sales to the gender and ages of their customers. The results of the last 3-month's sales are as follows:

Age (in years)
Gender Under 20 20 to 40 Over 40
Female 27 41 14
Male 12 34 22

a. What is the probability of randomly selecting a sale to someone over 40 given that it was a male customer?
b. What is the probability that the randomly selected sale was to someone under 20 and was a female customer?
c. What is the probability that the randomly selected sale was to someone who was between 20 and 40 or was a female customer?
d. What is the probability that the randomly selected sale was to a male customer

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The solution provides answers to numerous questions revolving around hypothesis testing, scatter diagrams and calculating test statistics.

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See Also This Related BrainMass Solution

Statistics: Construct and analyze Scatter Diagrams

11. Make up a scatter diagram with 10 dots for each of the following situations:

(a) perfect positive linear correlation,
(b) large but not perfect positive linear correlation,
(c) small positive linear correlation,
(d) large but not perfect negative linear correlation,
(e) no correlation,
(f) clear curvilinear correlation.

For problem 12, do the following:
(a) Make a scatter diagram of the scores;
(b) describe in words the general pattern of correlation, if any;
(c) figure the correlation coefficient;
(d) figure whether the correlation is statistically significant (use the .05 significance level, two-tailed);
(e) explain the logic of what you have done, writing as if you are speaking to someone who has never heard
of correlation (but who does understand the mean, deviation scores, and hypothesis testing); and
(f) give three logically possible directions of causality, indicating for each direction whether it is a reasonable explanation for the correlation in light of the variables involved (and why).

12. Four research participants take a test of manual dexterity (high scores mean
better dexterity) and an anxiety test (high scores mean more anxiety). The
scores are as follows.

Person Dexterity Anxiety
1 1 10
2 1 8
3 2 4
4 4 - 2

18. Twenty students randomly assigned to an experimental group receive an instructional
program; 30 in a control group do not. After 6 months, both groups
are tested on their knowledge. The experimental group has a mean of 38 on the
test (with an estimated population standard deviation of 3); the control group
has a mean of 35 (with an estimated population standard deviation of 5).

Using the .05 level, what should the experimenter conclude?
(a) Use the steps of hypothesis testing,
(b) sketch the distributions involved, and
(c) explain your answer to someone who is familiar with the t test for a single sample, but not with
the t test for independent means.

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