1.) A recent study of 100 individuals revealed that in the US the mean amount of money spent on gifts for Mother’s Day for a given individual is $38. The population standard deviation is not known but is estimated to be $12.

a.) Using a 90% confidence, what is the margin of error in estimating the mean?

b.) Using your results from part (a), what is the 90% confidence interval for the mean? Interpret your results.

c.) How many individuals need to be sampled in order to have a margin of error of $1.2 at 90% confidence

2.) Suppose a survey reveals that 12 out of 1500 individuals are a twin.

a.) What is the point estimate of the population proportion?

b.) Using a 95% confidence, what is the margin of error in estimating the population proportion?

c.) Using your results from part (b), what is the 95% confidence interval for the population proportion?

3.) In the United States, the mean monthly electric bill is $250 per household. A sample of 100 households is taken and showed a sample mean of $247.60. Suppose the population standard deviation is $10.00. Suppose you wish to determine if the mean monthly electric bill is under $250 per household. Assume the probability of a Type I error is 0.05.

a.) State the null and alternative hypotheses.

b.) What is the value of the test statistic?

c.) What is the p-value?

d.) State your conclusions.