Question

According to a study done by Wakefield Research, the proportion of Americans who can order a meal in a foreign language is 0.47. Would it be unusual that, in a survey of 200 Americans, 80 or fewer Americans can order a meal in a foreign language? Justify your answer. According to a study done by Wakefield Research, the proportion of Americans who can order a meal in a foreign language is 0.47. Would it be unusual that, in a survey of 200 Americans, 80 or fewer Americans can order a meal in a foreign language? Justify your answer

Answer 1

The following information has been provided about the population proportion and the sample size:

Population Proportion =	0.47
Sample Size =	200

80/200 = 0.4

We need to compute . Based on the information provided, the population men of sample proportions and the corresponding standard error are:

Observe that:

which indicates that the assumption for normal approximation for the sampling distribution is met.

Now, the following is obtained using normal approximation:

Since, z > -3

hence, it is not unusual