Statistics Questions

These are due monday July 15, 2013 at 11:00 PM eastern time….

 

questions are attached in wordpad format

1. (

2. The conditions on paired sample data for performing a hypothesis test or constructing a confidence interval on paired sample data are that the population is _______ or the sample size is ________.

3. ______ [notation] represents the sample mean of the set of n paired differences.

4. What statistic is used to estimate the common unknown population proportion?

5. Trying to quit smoking? Butt-Enders, a cigarette dependence reduction program, claims to lower the average number of cigarettes smoked for it’s participants. A sample of 10 participants consumed the following numbers of cigarettes on a randomly chosen day before and after attending Butt-Enders. Assume that the differences are normally distributed.

Participant——-1—-2—–3—-4—–5—–6—–7—–8—–9—–10

Before ———-40—20—60—30—-50—-60—20—-40—30—–20

After ————20—0—-40—30—-20—-60—20—-20—-0——20

a) find a 90% confidence interval for the population mean difference in number of cigarettes smoked.

b) use your confidence interval to test at level of significance α = 0.10 whether the population mean difference in number of cigarettes smoked differs from 0.

Use this information on exercise 12. A soft drink company recently performed a major overhaul of one of its bottling machines. Management is eager to determine whether the overhaul has resulted in an increase in productivity for the machine. One hundred “minute segments” are sampled at random from the updated machine (Sample 1) and a machine which was not updated (Sample 2), and the number of bottles processed is noted. The mean and the standard deviation of the number of bottles processed by each machine is given in the table.

Updated Machine———-n1=100————x1(with line over the x) = 200————–s1 = 30

Non Updated Machine—–n2=100————x2(with line over the x) = 190————–s2 = 25

6. Construct and interpret a 95% confidence interval for μ1 – μ2.

7. The U.S. Census Bureau reported in 2002 that, for people 18-24 years old, the mean annual income for people who never married was $13,539 and for married people was $19,321. Suppose that this information came from a survey of 100 people from each group and that the sample standard deviations were $5000 for the people who never married and $8000 for the married people.

a) test at level of significance α = 0.10 whether the population mean income for never married people differs from that of married people.

b) if we construct a 90% confidence interval for μ1 – μ2, will the interval include 0? Explain why or why not.

c) confirm your statements from (b).

8. Are fewer people getting married? The U.S. Census Bureau reported that in 1990, 74.1% of people aged 35-44 were married, while in 2000, 69% of people aged 35-44 were married. Assume that the data are from random samples of size 1000 each. Test whether the population proportion of people aged 35-44 who were married was lower in 2000 than in 1990, using level of significance α = 0.05.