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9. Telephone Interviews: Survey The National Study of the Changing Work Force conducted an extensive survey of 2958 wage and salaried workers on issues ranging from relationships with their bosses to household chores. The data were gathered through hour-long telephone interviews with a nationally representative sample (The Wall Street Journal). In response to the question “What does success mean to you?” 1538 responded, “Personal satisfaction from doing a good job.” Let p be the population proportion of all wage and salaried workers who would respond the same way to the stated question. Find a 90% confidence interval for p.

10. Telephone Interviews: Survey How large a sample is needed in Problem 9 if we wish to be 95% confident that the sample percentage of those equating success with personal satisfaction is within 1% of the population percentage? Hint: Use p < 0.52 as a preliminary estimate.

Peppers The following data represent soil water content (percent water by volume) for independent random samples of soil taken from two experimental fields growing bell peppers

Agricultural, Biological, and Environmental Statistics). Note: These data are also available for download at the Componion Sites for this Text. Soil water content from field I: x1; n1 5 72 15.1 11.2 10.3 10.8 16.6 8.3 9.1 12.3 9.1 14.3 10.7 16.1 10.2 15.2 8.9 9.5 9.6 11.3 14.0 11.3 15.6 11.2 13.8 9.0 8.4 8.2 12.0 13.9 11.6 16.0 9.6 11.4 8.4 8.0 14.1 10.9 13.2 13.8 14.6 10.2 11.5 13.1 14.7 12.5 10.2 11.8 11.0 12.7 10.3 10.8 11.0 12.6 10.8 9.6 11.5 10.6 11.7 10.1 9.7 9.7 11.2 9.8 10.3 11.9 9.7 11.3 10.4 12.0 11.0 10.7 8.8 11.1 Soil water content from field II: x2; n2 5 80 12.1 10.2 13.6 8.1 13.5 7.8 11.8 7.7 8.1 9.2 14.1 8.9 13.9 7.5 12.6 7.3 14.9 12.2 7.6 8.9 13.9 8.4 13.4 7.1 12.4 7.6 9.9 26.0 7.3 7.4 14.3 8.4 13.2 7.3 11.3 7.5 9.7 12.3 6.9 7.6 13.8 7.5 13.3 8.0 11.3 6.8 7.4 11.7 11.8 7.7 12.6 7.7 13.2 13.9 10.4 12.8 7.6 10.7 10.7 10.9 12.5 11.3 10.7 13.2 8.9 12.9 7.7 9.7 9.7 11.4 11.9 13.4 9.2 13.4 8.8 11.9 7.1 8.5 14.0 14.2 (a) Use a calculator with mean and standard deviation keys to verify that x1 < 11.42, s1 < 2.08, x2 < 10.65, and s2 < 3.03.

(b) Let m1 be the population mean for x1 and let m2 be the population mean for x2. Find a 95% confidence interval for m1 2 m2.

(c) Interpretation Explain what the confidence interval means in the context of this problem. Does the interval consist of numbers that are all positive? all negative? of different signs? At the 95% level of confidence, is the population mean soil water content of the first field higher than that of the second field?

(d) Which distribution (standard normal or Student’s t) did you use? Why? Do you need information about the soil water content distributions?

Answer #1

We want to compare the
soil water content (% water by volume) of two fields growing bell
peppers.
The claim is that the two fields have different soil water
content.
Use the data below to test the hypothesis that the fields have
different soil water content.
Field 1 is in list1 and Field 2 is in list2.
We do not know whether the water content values are normally
distributed or not, but their variances are equal.
Provide your answers below....

The following data represent soil water content (percentage of
water by volume) for independent random samples of soil taken from
two experimental fields growing bell peppers.
Soil water content from field I: x1; n1 = 72
15.2 11.3 10.1 10.8 16.6 8.3 9.1 12.3 9.1 14.3 10.7 16.1 10.2
15.2 8.9 9.5 9.6 11.3 14.0 11.3 15.6 11.2 13.8 9.0 8.4 8.2 12.0
13.9 11.6 16.0 9.6 11.4 8.4 8.0 14.1 10.9 13.2 13.8 14.6 10.2 11.5
13.1 14.7 12.5...

The following data represent soil water content (percentage of
water by volume) for independent random samples of soil taken from
two experimental fields growing bell peppers.
Soil water content from field I: x1; n1 = 72
15.2 11.3 10.1 10.8 16.6 8.3 9.1 12.3 9.1 14.3 10.7 16.1 10.2
15.2 8.9 9.5 9.6 11.3 14.0 11.3 15.6 11.2 13.8 9.0 8.4 8.2 12.0
13.9 11.6 16.0 9.6 11.4 8.4 8.0 14.1 10.9 13.2 13.8 14.6 10.2 11.5
13.1 14.7 12.5...

The following data represent soil water content (percentage of
water by volume) for independent random samples of soil taken from
two experimental fields growing bell peppers. Soil water content
from field I: x1; n1 = 72 15.2 11.3 10.1 10.8 16.6 8.3 9.1 12.3 9.1
14.3 10.7 16.1 10.2 15.2 8.9 9.5 9.6 11.3 14.0 11.3 15.6 11.2 13.8
9.0 8.4 8.2 12.0 13.9 11.6 16.0 9.6 11.4 8.4 8.0 14.1 10.9 13.2
13.8 14.6 10.2 11.5 13.1 14.7 12.5...

An important statistical measurement in service facilities (such
as restaurants and banks) is the variability in service times. As
an experiment, two bank tellers were observed, and the service
times for each of 100 customers were recorded. Do these data allow
us to infer at the 5% significance level that the variance in
service times differs between the two tellers? Estimate with 95%
confidence the ratio of variances of the two bank tellers. Teller 1
Teller 2 7.2 10.9 5.4...

The pathogen Phytophthora capsici causes bell peppers to wilt
and die. Because bell peppers are an important commercial crop,
this disease has undergone a great deal of agricultural research.
It is thought that too much water aids the spread of the pathogen.
Two fields are under study. The first step in the research project
is to compare the mean soil water content for the two fields. Units
are percent water by volume of soil.
Field A samples, x1: 10.2 10.7...

To test for any significant difference in the number of hours
between breakdowns for four machines, the following data were
obtained.
Machine
1
Machine
2
Machine
3
Machine
4
6.4
8.8
10.9
9.7
7.9
7.6
10.3
12.6
5.5
9.5
9.6
11.8
7.5
10.3
10.2
10.7
8.4
9.3
9.0
11.0
7.5
10.3
8.8
11.4
a) Use Fisher's LSD procedure to test for the equality of the
means for machines 2 and 4. Use a 0.05 level of significance.
Find the value...

Use the data in Bank Dataset to answer this question.
Construct a 95% confidence interval for the mean increase in
deposits. Note that the population standard deviation σ is not
known in this case. Instead the sample standard deviation s should
be calculated from the sample and the t distribution should be
used.
2. What is the margin of error at the 95% confidence level?
Bank Dataset of Increase in deposits. Mean is 4. Sample size is
152 customers.
4.3...

Steady-state hemoglobin levels were measured on a total of N =
41 patients with k = 3 types of sickle cell disease. The k = 3
types are HB SS, HB ST (HB S/-thalassemia), and HB SC. The
resulting data are displayed in Table 12.3.
SS
7.2
7.7
8.0
8.1
8.3
8.4
8.4
8.5
8.6
8.7
9.1
9.1
9.1
9.8
10.1
10.3
ST
8.1
9.2
10.0
10.4
10.6
10.9
11.1
11.9
12.0
12.1
SC
10.7
11.3
11.5
11.6
11.7
11.8...

Steady-state hemoglobin levels were measured on a total of N =
41 patients with k = 3 types of sickle cell disease. The k = 3
types are HB SS, HB ST (HB S/-thalassemia), and HB SC. The
resulting data are displayed in Table 12.3.
SS
7.2
7.7
8.0
8.1
8.3
8.4
8.4
8.5
8.6
8.7
9.1
9.1
9.1
9.8
10.1
10.3
ST
8.1
9.2
10.0
10.4
10.6
10.9
11.1
11.9
12.0
12.1
3
SC
10.7
11.3
11.5
11.6
11.7...

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