In 2003 the Gerber company sponsored a large random survey o

In 2003, the Gerber company sponsored a large random survey of the eating habits of American infants and toddlers. Among the many questions parents were asked was whether their child had eaten fried potatoes on the day before the interview. Of the 655 infants 9 to 11 months old in the study, 9% had eaten fried potatoes that day.

A) Calculate a 90% confidence interval for p:

B) Which of the following assumptions are needed for the interval in (a) to be valid? Select all that apply.

The data are obtained randomly.

The original population is normally distributed.

The sample size is large enough so that the number of successes and the number of failures are both at least 15.

The sample size is large enough so that the number of successes and the number of failures are both less than 15.

Solution

sol)

Given

Sample proportion = p=9% =0.09

Sample size = n=655

90% confidence interval for p:

=(p-Z_alpha sqrt(pq/n) , p+Z_alpha sqrt(pq/n)) where Z alpha=1.645 at 90% level

=(0.0716, 0.1084)

90% confidence interval for p: is (0.0716, 0.1084)

B) Here

*There data are obtained randomly is True. Because all the procedure satisfies this condition

**The orginal population is normally distributed is False .Because Since here sample size is morethan 30.

Hence we need not make this assumption

*** The sample size is large enough so that the number of success and the number of failures are both atleast 15 is True. In this case they (61 and 614) . So we sample size may be very large

****The sample size is large enough so that the number of success and the number of failures are both less than 15 is False.