# Expert Answers - Choose the one alternative

1.  Choose the one alternative that best completes the statement or answers the question.
Assume independent random samples are available from two populations giving information about population proportions. For the first sample assume n1= 100 and x1= 45. For the second sample, assume n2= 100 and x2= 42. Use the given sample sizes and numbers to find the pooled estimate of p̄. Round your answer to the nearest thousandth.

0.479
0.305
0.435
0.392

2.  Choose the one alternative that best completes the statement or answers the question.
Assume two independent random samples are available which provide sample proportions. For the first sample assume n1= 100 and x1= 42. For the second sample, assume n2= 100 and x2= 45. Test the null hypothesis that the population proportions are equal versus the alternative hypothesis that the proportion for population 2 is greater than the proportion for population 1.  Frame the null hypothesis as H0 : p2 – p1 = 0, and the alternative as HA : p2 – p1 0.  Pick the correct z value and p-value.  Round your answer to the nearest thousandth.

-0.428 p-value= 0.334
0.428 p-value= 0.668
0.428 p-value= 0.334
-0.428 p-value= 0.668

3. Construct the indicated confidence interval for the difference between the two population means. Assume that the two samples are independent simple random samples selected from normally distributed populations.  Assume that the population standard deviations are equal.
Two types of flares are tested and their burning times are recorded. The summary statistics are given below.
Brand X  n = 35  mean = 19.4 minutes  standard deviation =1.4 minutes
Brand Y  n = 40  mean = 15.1 minutes  standard deviation = 1.3 minutes
Construct a 95% confidence interval for the differences between the mean burning time of the brand X flare and the mean burning time of the brand Y flare.
3.2 min < µX - µY < 5.4 min
3.7 min < µX - µY < 4.9 min
3.5 min < µX - µY < 5.1 min
3.9 min < µX - µY < 4.7 min

4. Construct a 95% confidence interval for the mean difference µd using a sample of paired data for which summary statistics are given. Assume the parent populations are normally distributed.  Assume the sample mean difference d = 3.0, the sample standard deviation sd = 2.911, and n = 8.

0.566 < µd < 5.434
0.691 < µd < 5.559
2.264 < µd < 3.986
0.691 < µd< 3.986

5.True or False
One-way Analysis of Variance is used to determine statistically whether the variance between the treatment level means is greater than the variances within levels (error variance).  It is assumed that the observations are random samples drawn from normally distributed populations that have equal variances.  (Refer to Business Statistics Section 11.2.)
True
False

Note: Although Analysis of Variance does compare the between-treatment variance with the within-treatment variance, the purpose of the test is to determine if the means of the groups are different, rather than the variances.

6. Use the given data to answer the question.
Identify the value of the test statistic.
DF          SS           MS         F             p
Factor   3             13.500   4.500     5.17       0.011
Error      16           13.925   0.870
Total      19           27.425
5.17
13.500
4.500
0.011

7.Solve the problem.
A manager at a bank is interested in comparing the standard deviation of the waiting times when a single waiting line is used versus when individual lines are used. He wishes to test the claim that the population standard deviation for waiting times when multiple lines are used is greater than the population standard deviation for waiting times when a single line is used. This is a test of differences in variability.  Find the p-value for a test of this claim given the following sample data. If you use R, you will be able to calculate a precise p-value.  If you do a table lookup, you won't be able to find the exact p-value, but will be able to bound the p-value.   Retain at least 4 digits in the calculated p-value if you use R.
Sample 1: multiple waiting lines: n1 = 13, s1 = 2.0 minutes
Sample 2: single waiting line: n2 = 16, s2 = 1.1 minutes

0.05 <= p-value < 0.1
0.025 <= p-value < 0.05
0.01 <= p-value < 0.025
0.005 <= p-value < 0.01

8.Provide an appropriate response.
Fill in the missing entries in the following partially completed one-way ANOVA table.
Source   df           SS           MS-SS/df             F-statistic
Treatment                         22.2
Error      26                         4
Total      31
Source   df           SS           MS-SS/df             F-statistic
Treatment           5            22.2       4.44       1.11
Error      26           104.0     4
Total      31           126.2
Source   df           SS           MS-SS/df             F-statistic
Treatment           5            22.2       4.44       0.90
Error      26           104.0     4
Total      31           126.2
Source   df           SS           MS-SS/df             F-statistic
Treatment           57          22.2       0.39       316.35
Error      26           104.0     4
Total      31           126.2
Source   df           SS           MS-SS/df             F-statistic
Treatment           5            22.2       4.44       1.11
Error      26           104.0     4
Total      31           22.35

9.use the given data to find the equation of the regression line.  Round the final values to three significant digits, if necessary.  Let x be the independent variable and y the dependent variable.  (Note that if x = 2, then y = 7 and so forth.  yhat is the predicted value of the fitted equation.)
x   2    4    5    6
y   7  11  13   20
yhat = 0.15 + 2.8x
yhat = 3.0x
yhat = 0.15 + 3.0x
yhat = 2.8x

10. Find the value of the linear correlation coefficient r using the data below.  ( Note that if x = 47.0 then y = 8, and so forth.)
x   47.0   46.6   27.4   33.2   40.9
y     8      10      10        5      10
0
-0.175
0.175
0.156