Question

In a study investigating the difference in food preferences between men and women, researchers asked subjects to indicate whether they like or disliked certain foods. One question was about lamb. Twenty percent of a sample of 75 men disliked lamb, while 38% of a sample of 100 women indicated that they disliked lamb. Test the claim that there is a difference in the proportions of men and women who dislike lamb.

Indicate the correct set of statistical hypotheses for this test.

What is the test statistic?

What is the p-value for this test?

What is your decision regarding the null?

Provide the confidence interval.

Please describe why the confidence interval and hypothesis test are consistent.

Answer 1

Let the sample proportion of men who dislike lamb be p1. Here p1=0.2 ; Let the sample size of men be n1=75.

Let the sample proportion of women who dislike lamb be p2. Here p2=0.38 ; Let the sample size of women be n2=100.

Let the population proportion of men who dislike lamb be P1 and the proportion of women who dislike lamb be P2.

Here we are to test

The test statistic is given by

where

Here ,

The p-value is 0.01046

As the p-value is less than 0.05, we reject the null hypothesis at 5% level of significance. Hence we conclude that both the proportions are not equal.

The upper confidence limit is given by

Here it is

The lower confidence limit is

Here it is

Now this is the confidence interval for the difference between the population proportion of men and female.

Hence this is consistent.

Both the hypothesis test and the confidence interval gives the result at 5% level of significance that the population proportions are significantly different.

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