1)

A survey of 196 Americans conducted in the year 2019 found that average beef consumption was 56 pounds, with a standard deviation of 50.

a) Calculate a 90% confidence interval for 2019 beef consumption.

b) Your colleague found a source that says in 1999, the average American consumed 64 pounds of beef. Conduct a hypothesis test of your sample mean described at the top of this page (sample mean 56, standard deviation 50, n = 196) against the benchmark of 64 that your colleague found. State your null and alternative hypothesis, calculate the test statistic, make a statement about your conclusion regarding the null hypothesis, and state whether we have sufficient evidence to claim that consumption habits have changed in the last 20 years. Use the 5% significance level. c) Would you reach the same conclusion (from part b) if we had used the 10% significance level? Why or why not? d) (From part b) What about the 1% significance level? Why or Why not? e) In what range does the p-value of the test statistic from part b fall a. Greater than 0.10 b. Between 0.05 and 0.10 c. Between 0.01 and 0.05 d. Less than 0.01

2)

A recent survey found that 60% (0.60) of Republicans (n1=160) support expanding development of nuclear energy versus 43% of Democrats (n2=186).

a. Calculate the 99% confidence interval for the proportion of Republicans who support expanding nuclear energy. b. Calculate the 99% confidence interval for the proportion of Democrats who support expanding nuclear energy. c. (BONUS) Calculate the 95% confidence interval for the difference between these two groups.

3)

An anthropologist is trying to determine if there is a significant difference between the average height of individuals in Country "A" vs. Country "B". In Country A, they survey 123 individuals with an average height of 179.2 cm (and a standard deviation of 6.1). In Country B, they survey 154 individuals with an average height of 178.1 cm (and a standard deviation of 5.8 cm). Test the null hypothesis that the average height in the two countries is equal (vs. the alternative that they are not equal). List your null and alternative hypotheses. Calculate your test statistic, make a statement about the null hypothesis (reject or not), and state whether we have sufficient evidence to claim that height in the two countries is different. Use the 5% significance level.