Assignment 11: 2 Sample Inference WS Name:

Neatly respond to each prompt. Show all work for full credit. Round to four decimal places.

1. A reading activity is introduced to help third graders improve their reading. A class of 21 students takes part in the activities for 8 weeks. A control class of 23 students has the same curriculum minus the activities. At the end of the 8 weeks, all students are given a reading test. The average and standard deviation of the treatment groups scores are 51.41 and 11.01 respectively. The average and standard deviation of the control group scores are 41.52 and 17.15 respectively. Is there evidence that the activities helped?

a. Which procedure would you use to analyze these data? Explain your choice.
Independent samples – general procedure
Independent samples – pooled variance procedure

b. Would it be possible to implement a paired sample experiment to aIDress the effectiveness of the reading activity for this unit in the curriculum? If so, describe a paired experiment. If not, explain why not.

2. Does calcium reduce blood pressure? A randomized comparative experiment gave one group of 10 men a calcium supplement for 12 weeks. The control group of 11 men received a placebo. The average decrease in blood pressure for the treatment group was 5 mm with sample standard deviation 8.743 mm. The average and standard deviation for the control (placebo) group were -0.273 mm and 5.901 mm respectively. Is there evidence of a difference between the two groups?
State whether you would treat the samples as paired or independent. If independent, would you use the general or pooled variance procedure to analyze the data? Explain
In general, why do we bother using the pooled variances procedure when the general procedure will work in any case?

3. Which of the following are true statements? (Circle all that apply).
The p-value is the probability that the null hypothesis is true.
If the p-value is large, we reject the null hypothesis.
A small p-value indicates evidence in favor of the null hypothesis.
A small p-value indicates that the observed data are unlikely if the null hypothesis is true.
If p=0.0001, the null hypothesis cannot be true.
If (-0.5, 0.5) is a 95% confidence interval for ?, we would fail to reject the null hypothesis in a size 0.05 test of H0: ? = 1.
4. A company has two production lines for constructing television sets. 1128 TV’s are randomly chosen from line A of which 23 fail to meet the company’s quality standards and 24 of 962 TVs randomly chosen from line B fail to meet the standards. We could conduct a hypothesis test to determine if this is evidence of a difference in operating standards between the two lines.

What are the population(s) and parameter(s) of interest?
If we reject the null hypothesis what do we conclude?

5. You conduct a hypothesis to compare the impact of two different training regimens (regimen 1 and regimen 2) on swimmers’ speeds. To this end, you consider 10 swimmers from each regimen and find the mean improvement in times.
a. If the symbols below are defined as usual, which is the appropriate null hypothesis stated symbolically?
H0:
H0: ?1 = ?2
H0: ?1 ? ?2
H0:
H0: p1 = p2

b. Which is the appropriate alternative hypothesis given in context?
The mean time improvement is the same for both regimens.
The mean time improvement is not the same for both regimens.
The proportion of swimmers who improved is the same for both regimens.
The proportion of swimmers who improved is not the same for both regimens.
6. A study examines whether male and female college students are equally likely to be frequent binge drinkers. The data (from Moore McCabe and Craig, p. 513) are given in the table below:

Population n X X/n
1 (men) 5,348 12,392 0.260
2 (women) 8,471 12,748 0.206
Let p1 be the proportion of male binge drinkers and let p2 be the proportion of female binge drinkers. The null and alternative hypotheses are H0: p1 = p2 and HA: p1 ? p2.

a. Obviously the two proportions 0.260 and 0.206 are different. Why can we not just reject the null hypothesis based on this observation without doing inference?

b. The p-value for this test is p=0.0004. State the conclusions.