1) For each of the following statements, formulate appropriate null and alternative hypotheses. Indicate whether the appropriate test will be one-tailed or two-tailed,then sketch a diagram that shows the approximate location of the rejection regions for the test.

a) The average college student spends no more than $300 per semester at the university's bookstore.

b) The average adult drinks 1.5 cups of coffee per day.

c) The average SAT score for entering freshmen is at least 1200.

d) The average employee put in 3.5 hours of overtime last week.

I have the answers for a) H0: u greater or equal to 300 H1: u < 300 so its a one tailed test. Draw the bell curve and shade the left side of it. That’s the rejection region

b) H0: u is = to 1.5
H1: u is not = to 1.5 this is the two tailed test. Reject the two sided of the bell curve but not the middle

Need the answer for C and D.

2) The International Coffee Association has reported the mean daily coffee consumption for U.S. residents as 1.65 cups. Assume that a sample of 38 people from a North Carolina city consumed a mean of 1.84 cups of coffee per day, with a standard deviation of 0.85 cups. In a two-tail test at the 0.05 level, could the residents of this city be said to be significantly different from their counterparts across the nation?

3) During 2002, college work study students earned a mean of $1252. Assume that a sample consisting of 45 of the work study students at a large unversity was found to have earned a mean of $1277 during that year, with a standard deviation of $210. Would a one-tail test at the 0.05 level syggest the average earnings of this university's work study students were significantly higher than the national mean?

I'll give you a few hints for 1).

Rethink part a). The statement says "no more than $300" which means $300 or less. You are correct in that this one is a one-tailed test.
Part b) looks good!
For part c): The statement is says "at least 1200" which means 1200 or more. (This test will be one-tailed.)
Part d) is similar to part b).

For 2): Use a one-sample z-test.
Here's a formula:
z = (sample mean - population mean)/(standard deviation divided by the square root of the sample size)
With the data:
z = (1.84 - 1.65)/(0.85/√38) = ?

Finish the calculation. Determine the critical or cutoff value to reject the null by looking at a z-table using 0.05 for a two-tailed test. If the test statistic exceeds either critical value (in either direction), then the null is rejected in favor of the alternative hypothesis. You can then conclude there is a difference. If the test statistic does not exceed either critical value, then the null is not rejected and you cannot conclude a difference.

For 3): Use the same process with the same formula as 2). Remember that this one is a one-tailed test, but the procedures to determine whether or not to reject the null are the same.

I hope this will help.

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To generate the appropriate null and alternative hypotheses for statements C and D, we need to consider the given information and the desired direction of the test:

c) The average SAT score for entering freshmen is at least 1200.
Null Hypothesis (H0): The average SAT score for entering freshmen is less than 1200.
Alternative Hypothesis (H1): The average SAT score for entering freshmen is greater than or equal to 1200.
This is a one-tailed test. We are interested in determining if the average SAT score is higher than the given value of 1200. Therefore, we will draw the bell curve and shade the right side of it, representing the rejection region.

d) The average employee put in 3.5 hours of overtime last week.
Null Hypothesis (H0): The average employee puts in exactly 3.5 hours of overtime last week.
Alternative Hypothesis (H1): The average employee does not put in exactly 3.5 hours of overtime last week.
Since the alternative hypothesis includes "does not equal to," this is a two-tailed test. We are interested in determining if the average overtime is different from the given value of 3.5 hours. Therefore, we will reject both sides of the bell curve but not the middle.

Now, let's move on to the next task:

2) To test if the residents of a North Carolina city are significantly different from the mean daily coffee consumption for U.S. residents (1.65 cups) at a significance level of 0.05, we can conduct a hypothesis test.

Null Hypothesis (H0): The mean daily coffee consumption for the North Carolina city residents is equal to the mean daily coffee consumption for U.S. residents (1.65 cups).
Alternative Hypothesis (H1): The mean daily coffee consumption for the North Carolina city residents is different from the mean daily coffee consumption for U.S. residents (1.65 cups).

We can perform a two-tail t-test, as we are interested in determining if the mean daily coffee consumption for the North Carolina city residents is significantly different (either higher or lower) than the mean for U.S. residents. With a sample size of 38 and a mean of 1.84 cups, and a known standard deviation of 0.85 cups, we can calculate the t-statistic. Using the critical value of 0.05 and the degrees of freedom (n-1), we can compare the calculated t-value to the critical value to determine if the residents of this city are significantly different from their counterparts across the nation.

3) To determine if the average earnings of a university's work-study students are significantly higher than the national mean (1252), we can perform a hypothesis test.

Null Hypothesis (H0): The average earnings of the university's work-study students are equal to the national mean (1252).
Alternative Hypothesis (H1): The average earnings of the university's work-study students are higher than the national mean (1252).

Based on the given information, we can conduct a one-tail test at a significance level of 0.05. With a sample size of 45 and a mean of 1277, along with a standard deviation of 210, we can calculate the t-statistic. Using the critical value of 0.05 and the degrees of freedom (n-1), we can compare the calculated t-value to the critical value to determine if the average earnings of this university's work-study students are significantly higher than the national mean.