Question

B: According US News, about 28% of Americans claim that they do not get enough sleep. Gallup feels that 28% is a low value so they conducted a poll that found that 30% of a random sample of 801 Americans responded that they do not get enough sleep. Perform an appropriate hypothesis test using α=0.05. Be sure to include the following:

1. State the null and alternative hypotheses in symbols and words. Assume conditions have been met. (2 pts.)
2. Perform your hypothesis test "by hand" using the equation editor. Be sure to use the appropriate probability notation. Don't write your conclusion in this step.(4 pts.)
3. Construct a 90% confidence interval, again showing calculations "by hand". Don't write your conclusion in this step. (4 pts.)
4. State your conclusion making sure to site whether we reject or fail to reject and what that means in context based on the p-value. Then support your conclusion with the results from your confidence interval. Be sure to note whether the hypothesized value falls in our interval and what that means. (3 pts.)

Answer 1

Let p denotes the true proportion of Americans claim that they do not get enough sleep.

i) and ii)

iii)

Since 0.28 lies within the confidence interval, so at 90% level of confidence or at 10% level of significance, we can conclude that the true proportion of Americans claim that they do not get enough sleep is not significantly different from 0.28