1.
Are there more broken bones in summer or winter? We get records about the number of fractures treated in January and July at a random sample of 25 emergency rooms.
The 95% confidence interval for the mean change ( μd = μJan - μJuly )in the numbers of fractures between January and July is (-2, 4)
Interpret the confidence interval.
A) We are 95% confident that there are fewer fractures treated in July than January.
B) We are 95% confident that the mean change in fractures treated between July and January was between 2 fewer and 4 more fractures treated.
C) We are 95% confident that each emergency room treats between 2 fewer and 4 more fractures when comparing July to January.
D) We are 95% confident that the mean change in fractures treated between January and July was between 2 fewer and 4 more fractures treated.
2.
Every year Educational Services (ETS) selects readers for the Advanced Placement Exams. Recently the AP Statistics exam has been graded in Lincoln, Nebraska. One objective of ETS is to achieve equity in grading by inviting teachers to be readers from all parts of the nation. However budgets are a constant issue also. The accountants at ETS wonder if the flights from cities west of Lincoln are the same as flight costs from cities east of Lincoln. A random sample of the expense vouchers from last year was reviewed for the cost of airline tickets.
Identify the null and alternative hypotheses.
A.
μEast - μWest ≠ 0
B.
μEast - μWest = 0
C.
μEast - μWest < 0
D.
μEast - μWest > 0
H0: (what letter)
HA: (what letter)
3.
Researchers developing new drugs must be concerned about possible side effects. They must check a new medication for arthritis to be sure that it does not cause an unsafe increase in blood pressure. They measure the blood pressures of a group of 12 subjects, then administer the drug and recheck the blood pressures one hour later.
Identify the null and alternative hypotheses.
A.
μAfter - μBefore > 0
B.
μAfter - μBefore < 0
C.
μd < 0 where μd = μAfter - μBefore
D.
μA - μB ≠ 0
E.
μd > 0 where μd = μAfter - μBefore
F.
μd = 0 where μd = μAfter - μBefore
G.
μAfter - μBefore = 0
H.
μd ≠ 0 where μd = μAfter - μBefore
H0: (what letter)
HA: (what letter)
Thank you!
1. D) We are 95% confident that the mean change in fractures treated between January and July was between 2 fewer and 4 more fractures treated.
2. H0: B) μEast - μWest = 0
HA: A) μEast - μWest ≠ 0
3. H0: F) μd = 0 where μd = μAfter - μBefore
HA: E) μd > 0 where μd = μAfter - μBefore
1. D) We are 95% confident that the mean change in fractures treated between January and July was between 2 fewer and 4 more fractures treated.
2. H0: B) μEast - μWest = 0
HA: A) μEast - μWest ≠ 0
3. H0: F) μd = 0 where μd = μAfter - μBefore
HA: C) μd < 0 where μd = μAfter - μBefore
1. The correct interpretation of the confidence interval is:
D) We are 95% confident that the mean change in fractures treated between January and July was between 2 fewer and 4 more fractures treated.
To arrive at this interpretation, we start by understanding what a confidence interval represents. In this case, we have a 95% confidence interval for the mean change in the numbers of fractures between January and July. This means that if we were to repeat this study multiple times, 95% of the resulting confidence intervals would include the true mean change in fractures.
The confidence interval given is (-2, 4), which means that based on the data from the random sample of 25 emergency rooms, we can be 95% confident that the true mean change in fractures treated between January and July falls within the range of 2 fewer fractures to 4 more fractures treated.
2. The correct null and alternative hypotheses for comparing flight costs from cities west of Lincoln to cities east of Lincoln are:
H0: μEast - μWest = 0 (Option B)
HA: μEast - μWest ≠ 0 (Option A)
The null hypothesis (H0) states that there is no difference in flight costs between cities east and west of Lincoln. The alternative hypothesis (HA) states that there is a difference in flight costs between the two regions.
3. The correct null and alternative hypotheses for checking if a new medication for arthritis causes an unsafe increase in blood pressure are:
H0: μd ≤ 0 where μd = μAfter - μBefore (Option C)
HA: μd > 0 where μd = μAfter - μBefore (Option E)
Here, we are comparing the blood pressures before and after administering the drug. The null hypothesis (H0) states that the mean difference in blood pressure (μd) is less than or equal to zero, implying that the drug does not cause an unsafe increase in blood pressure. The alternative hypothesis (HA) states that the mean difference in blood pressure is greater than zero, indicating that the drug does cause an unsafe increase.