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# Questions about Statistics: Correlation to hypothesis test

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Does correlation equal causation? Why or why not?

What is the relationship between correlation and association?

What is association?

When would you use regression correlation at your place of employment, in your education, or in politics?

How do you identify outliers in your data?

What are the differences between a two-tail test and a single (or one) tail test?

What is a variable?

What is variance?

Define the term reliability.

Why is a t-statistic, as opposed to a z-statistic, used to test small populations?

Why should the alternate hypothesis be the opposite of the null?

How many alternate hypotheses can we have?

Why do we state that we fail to reject the null - instead of simply saying that we have proven the null?

What do you do when testing two populations, and one sample's size is small and the other sample's size is large?

What do the following symbols represent? (this question counts for 30 points)
a) H0 =

b) H1 =

c) S (Uppercase Sigma) =

d) s (Lowercase Sigma) =

e) s =

f) s2 =

g) X bar (x-bar) =

h) alpha =

#### Solution Preview

Hello -

1.) Does correlation equal causation? Why or why not?

Correlation does not equal causation. Correlation means that there is a relationship between two variables, but not that one caused the other.

2.) What is the relationship between correlation and association?

Correlation is a measure of linear association between variables. In fact, the correlation coefficient, r, measures this linear association between two variables.

3.) What is association?

In general, two variables are associated if some of the variability of one can be accounted for by the other variable.

4.) When would you use regression correlation at your place of employment, in your education, or in politics?

In Politics, for example, you might try to find a correlation between IQ score and Politician voted for. Maybe an association could be found between IQ scores and voting Democrat or Republican.

5.) How do you identify outliers in your data?

A good way to identify outliers in data is to visually inspect the ...

#### Solution Summary

The solution provides answers to a series of questions relating to basic Statistics. Questions cover topics such as outliers, hypothesis testing, regression, and correlation.

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## Testing of hypothesis problems

Question 1
For the given data, find (a) the point estimate of the population mean and (b) the margin of error for a 90% confidence interval. Lengths of work commute of 32 people (in miles):
12 9 7 2 8 7 3 27
21 10 13 3 7 2 30 7
6 13 6 14 4 1 10 3
13 6 2 9 2 12 16 18

Question 2
a. Find the critical value of tc for the confidence level c and the sample size n, noted below , using a two-sided test. C = 0.80 ; n = 22

b. Given c = 0.95 ; s = 0.05 ; n = 25 ; x(bar) = 3.5 (i) Find the margin of error. (ii)
Construct the confidence interval for &#956; using the statistics you have calculated above.

Question 3
Use a P- value to test the claim about the population mean &#956; using the given sample statistics. State your decision for &#945; = 0.05 Claim: &#956; &#8800; 230; Other values: x (bar) = 221.5 ; n = 36 ; and s - 17.3

Question 4
Use a t-test to investigate the claim and assume that the population is normally distributed:
A large university says the mean number of classroom hours per week for full-time faculty is more than 9. A random sample of the number of classroom hours for fulltime faculty for one week is listed. At &#945; = 0.05 , test the university's claim.
10.7 9.8 11.6 9.7 7.6 11.3 14.1 8.1 11.5 8.5 6.9

Question 5
Use the given sample statistics to test the claim about the difference between two population means &#956;1 and &#956;2 at the given level of significance &#945;. Assume the samples are random and independent and that the populations are approximately normally distributed, and that the population variances are unequal.
Claim: &#956;1 &#8805; &#956;2, &#945; = 0.1. Sample statistics:
x1 (bar) = 520, s1 = 25, n1 = 7
x2 (bar) = 500, s2= 55, n2 = 6

Question 6
Using a test for paired data, test the claim about the mean of the difference of the two populations at the given level of significance &#945; = 0.01 using the given statistics. Assume the populations are normally distributed, and that the population variances are unequal.
Claim: &#956;d < 0, &#945; = 0.01. Sample statistics:
d(bar) = 3.2, sd = 1.38, n1 = 25

Question 7
It is asserted that a greater proportion of males (= x 1 ) contribute to charity than females (= x 2 ). A survey of male and female contributors to charity showed that of 900 males surveyed, 86 contributed to charity, and of 1200 females surveyed, 107 contributed to charity. Assume the sample statistics are from random, independent samples.

State the Null, and Alternative , hypotheses to be tested, noting whether the test is a right-tailed, left-tailed , or two tailed test and test the hypothesis that the proportion of charitable givers are the same for both males and females. Test at the level &#945; = 0.05.

Question 8
Use the given contingency table to
(a) Find the expected frequencies of each cell in the table,
(b) Perform a chi-square test for independence, and
(c) Comment on the relationship between the two variables. Assume the variables are independent. The contingency table shows the results of a random sample of 500 individuals classified by gender and type of vehicle owned. Use &#945; = 0.01.

Question 9
The number of convertibles sold at a car dealership in a month and the average monthly temperature (in degree Fahrenheit) are given in the Table below :
a. Find the sample correlation coefficient r?
b. Determine whether there is a positive linear correlation, a negative linear correlation, or no correlation between the variables, and explain the results,
Convertible sold,
x 0 2 6 5 7 9
Average monthly temperature, y 40 48 58 62 72 79 noting particularly which variable is the dependent, and which the independent, one.
c. Is there enough evidence to conclude that there is a linear correlation between the number of convertibles sold and the average monthly temperature?
Use &#945; = 0.05 and show your work.

Question 10
A financial services institution claims that the median credit card debt among families with annual earnings of \$10,000 to \$24,999 is more than \$1200. The credit card debts (in thousands of dollars) among 13 randomly selected families are listed below. At &#945; = 0.01, can you support the institution's claim?
1.97 1.10 1.02 1.05 0.98 1.36 1.74 1.69 1.48 0.99 1.29 0.92 1.45
Use a sign test to test the claim by doing the following:
a. Write the claim mathematically and identify Ho and Ha.
b. Determine the critical value.
c. Calculate test statistics.
d. Decide whether to reject or fail to reject the null hypothesis.
e. Interpret the decision in the context of the original claim.

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