Homework Sourse12 The data below are yields for two different types of corn
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The data below are yields for two different types of corn seed that were used on adjacent plots of land. Assume that the data are simple random samples and that the differences have a distribution that is approximately normal. Construct a 95% confidence interval estimate of the difference between type 1 and type 2 yields. What does the confidence interval suggest about farmer Joe\'s claim that type 1 seed is better than type 2 seed?
Type_1 Type_2
1986 2003
1984 1917
2154 2082
2513 2454
2166 2164
1980 1902
2179 2139
1452 1489
In this example,?
?d?
is the mean value of the differences d for the population of all pairs of data, where each individual difference d is defined as the type 1 seed yield minus the type 2 seed yield.
The 95% confidence interval is?
____<?d< ____
(Round to two decimal places as needed.)
What does the confidence interval suggest about farmer Joe\'s claim that type 1 seed is better than type 2 seed?
A.
Because the confidence interval?
includes?
zero, there?
is?
sufficient evidence to support farmer Joe\'s claim.
B.
Because the confidence interval?
only includes positive values and does not include?
zero, there?
is?
sufficient evidence to support farmer Joe\'s claim.
C.
Because the confidence interval?
only includes positive values and does not include?
zero, there?
is not?
sufficient evidence to support farmer Joe\'s claim.
D.
Because the confidence interval?
includes zero, there is not?
sufficient evidence to support farmer Joe\'s claim.
Solution
======12=====
The data below are yields for two different types of corn seed that were used on adjacent plots of land. Assume that the data are simple random samples and that the differences have a distribution that is approximately normal. Construct a 95% confidence interval estimate of the difference between type 1 and type 2 yields. What does the confidence interval suggest about farmer Joe\'s claim that type 1 seed is better than type 2 seed?
Type_1 Type_2
1986 2003
1984 1917
2154 2082
2513 2454
2166 2164
1980 1902
2179 2139
1452 1489
Confidence Interval Estimate for the Mean
Data
Sample Standard Deviation
44.3814
Sample Mean
33
Sample Size
8
Confidence Level
95%
Intermediate Calculations
Standard Error of the Mean
15.6912
Degrees of Freedom
7
t Value
2.3646
Interval Half Width
37.1038
Confidence Interval
Interval Lower Limit
-4.10
Interval Upper Limit
70.10
In this example,?
?d?is the mean value of the differences d for the population of all pairs of data, where each individual difference d is defined as the type 1 seed yield minus the type 2 seed yield.
The 95% confidence interval is?
-4.10 < d < 70.10
(Round to two decimal places as needed.)
What does the confidence interval suggest about farmer Joe\'s claim that type 1 seed is better than type 2 seed?
A.Because the confidence interval includes zero, there is sufficient evidence to support farmer Joe\'s claim.
B. Because the confidence interval only includes positive values and does not include zero, there
Is sufficient evidence to support farmer Joe\'s claim.
C. Because the confidence interval only includes positive values and does not include zero, there is not sufficient evidence to support farmer Joe\'s claim.
D. Because the confidence interval includes zero, there is not sufficient evidence to support farmer Joe\'s claim.
| Confidence Interval Estimate for the Mean | |
| Data | |
| Sample Standard Deviation | 44.3814 |
| Sample Mean | 33 |
| Sample Size | 8 |
| Confidence Level | 95% |
| Intermediate Calculations | |
| Standard Error of the Mean | 15.6912 |
| Degrees of Freedom | 7 |
| t Value | 2.3646 |
| Interval Half Width | 37.1038 |
| Confidence Interval | |
| Interval Lower Limit | -4.10 |
| Interval Upper Limit | 70.10 |
