Question

Hypothesis Test - Two Proportions

            Sample

            Size   Successes   Proportion

Females        200          64      0.32000

Males          200          42      0.21000

Difference                         0.11000

Null Hypothesis: p1 = p2

Alternative Hyp: p1 ≠ p2

SE (difference) 0.04413

Z (uncorrected)    2.49    P 0.0127

93% Confidence Interval of Difference

0.03066 < p1-p2 < 0.18934

1. Use the confidence interval to make a statement about the relationship between these two proportions (in the words of the problem)? Make sure to include your reliability level in your answer. (4 points)

2. Suppose it is desired to reduce the interval width in this problem. What two choices can you make to accomplish this goal? (4 points)

3. What assumptions are needed for this analysis to be valid? (2 points)

Answer 1

ANSWER::

a)

We are to test if there is a difference between the two proportion or not

93% confidence interval for the difference betweeen the two proportion is

here we are 93% confident that the true difference between the prportion will lie within the interval above.

clearly the interval excludes zero which clearly indicate that there is a difference between the two proportion

Thus we can reject the null hypothesis in favour of the alternate hypothesis.

b)

width of the interval is 2* margin of error

to reduce the margin of error you can

1) increase the sample size

2) reduce the onfidence level.

c)

Two assumption is required :

random sampling should be done.

number of success and number of failure is greater than 10.

(OR) TRY THIS ANSWER

From the given data,

a)

Confidence interval of difference = (0.03066, 0.18934)

Since, the confidence interval does not contain zero, there is significant difference between the proportions of males and females that had a tattoo.

b)

The two choices are:

1) Increasing the sample size

2) Reducing the variability

c)

Here, the test used is two proportion z test

i) Sample size must be greater than 30 for both samples

ii) data should be selected randomly from a population where each has equal chance of being selected

iii) The data should be normal.

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