Random samples of size 225 are drawn from a population in which the proportion
with the characteristic of interest is 0.25. Decide whether or not the sample size is
large enough to assume that the sample proportion p̂is normally distributed.

 

 

When 2 births are randomly selected, the sample space for genders is bb, bg, gb, and gg. Assume that those 4 outcomes are equally likely. Construct a table that describes the sampling distribution of the sample proportion of girls from 2 births. Does the mean of the sample proportions equal the proportion of girls in 2 births? Does the result suggest that a sample proportion is an unbiased estimator of a population proportion?

6. As the test statistic becomes larger, the p-value

(a) gets smaller

(b) becomes larger 

(c) stays the same, since the sample size has not been changed

(d) becomes negative.

7. To describe the sampling distribution of the sample proportion, we use

(a) The sample proportion 

(b) The population proportion 

(c) The population mean

(d) The population mean

8. When small samples are used to estimate a population mean, in cases where the population standard deviation is unknown and the original distribution is normal:

(a) There always will be a large amount of sampling error.

(b) the t-distribution must be used to obtain the critical value.

(c) the resulting margin of error for a confidence interval estimate will tend to be fairly small.

(d) the z distribution must be used to obtain the critical value.

The population proportion is  . What is the probability that a sample proportion will be within   of the population proportion for each of the sample sizes ?