Question

The following data represent petal lengths (in cm) for independent random samples of two species of Iris. Petal length (in cm) of Iris virginica: x1; n1 = 35 5.0 5.7 6.2 6.1 5.1 5.5 5.3 5.5 6.9 5.0 4.9 6.0 4.8 6.1 5.6 5.1 5.6 4.8 5.4 5.1 5.1 5.9 5.2 5.7 5.4 4.5 6.4 5.3 5.5 6.7 5.7 4.9 4.8 5.8 5.2 Petal length (in cm) of Iris setosa: x2; n2 = 38 1.6 1.6 1.4 1.5 1.5 1.6 1.4 1.1 1.2 1.4 1.7 1.0 1.7 1.9 1.6 1.4 1.5 1.4 1.2 1.3 1.5 1.3 1.6 1.9 1.4 1.6 1.5 1.4 1.6 1.2 1.9 1.5 1.6 1.4 1.3 1.7 1.5 1.5 (a) Use a calculator with mean and standard deviation keys to calculate x1, s1, x2, and s2. (Round your answers to two decimal places.) x1 = s1 = x2 = s2 = (b) Let μ1 be the population mean for x1 and let μ2 be the population mean for x2. Find a 99% confidence interval for μ1 − μ2. (Round your answers to two decimal places.) lower limit upper limit (c) 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 99% level of confidence, is the population mean petal length of Iris virginica longer than that of Iris setosa? Because the interval contains only positive numbers, we can say that the mean petal length of Iris virginica is longer. Because the interval contains only negative numbers, we can say that the mean petal length of Iris virginica is shorter. Because the interval contains both positive and negative numbers, we cannot say that the mean petal length of Iris virginica is longer. (d) Which distribution did you use? Why? The Student's t-distribution was used because σ1 and σ2 are known. The standard normal distribution was used because σ1 and σ2 are known. The standard normal distribution was used because σ1 and σ2 are unknown. The Student's t-distribution was used because σ1 and σ2 are unknown. Do you need information about the petal length distributions? Explain. Both samples are small, so information about the distributions is not needed. Both samples are large, so information about the distributions is needed. Both samples are small, so information about the distributions is needed. Both samples are large, so information about the distributions is not needed.

Answer #1

a) Mean(x_{1})=5.48 ,SD(x_{1})=.56,
Mean(x_{2})= 1.48 SD(x_{2})= .20

b) Assuming normality and equal variance, a t distribution with DF=35+38-2=71 based 99% confidence interval comes out as

lower limit= 3.74, upper limit=4.25

c) Correct Option "Because the interval contains only positive numbers, we can say that the mean petal length of Iris virginica is longer."

d) Correct Option "The Student's t-distribution was used because σ1 and σ2 are unknown"

e) Correct Option "Both samples are large, so information about the distributions is not needed."

For any query, comment.

The following data represent petal lengths (in cm) for
independent random samples of two species of Iris.
Petal length (in cm) of Iris virginica:
x1; n1 = 35
5.3
5.9
6.5
6.1
5.1
5.5
5.3
5.5
6.9
5.0
4.9
6.0
4.8
6.1
5.6
5.1
5.6
4.8
5.4
5.1
5.1
5.9
5.2
5.7
5.4
4.5
6.4
5.3
5.5
6.7
5.7
4.9
4.8
5.7
5.2
Petal length (in cm) of Iris setosa:
x2; n2 = 38
1.6
1.9
1.4
1.5
1.5
1.6...

The following data represent petal lengths (in cm) for
independent random samples of two species of Iris.
Petal length (in cm) of Iris virginica: x1; n1
= 35
5.1 5.5 6.2 6.1 5.1 5.5 5.3 5.5 6.9 5.0 4.9 6.0 4.8 6.1 5.6 5.1 5.6
4.8 5.4 5.1 5.1 5.9 5.2 5.7 5.4 4.5 6.4 5.3 5.5 6.7 5.7 4.9 4.8 5.8
5.1
Petal length (in cm) of Iris setosa: x2; n2
= 38
1.4 1.6 1.4 1.5 1.5 1.6...

1. The following data represent petal lengths (in cm) for
independent random samples of two species of Iris.
Petal length (in cm) of Iris virginica:
x1; n1 = 35
5.1
5.9
6.1
6.1
5.1
5.5
5.3
5.5
6.9
5.0
4.9
6.0
4.8
6.1
5.6
5.1
5.6
4.8
5.4
5.1
5.1
5.9
5.2
5.7
5.4
4.5
6.4
5.3
5.5
6.7
5.7
4.9
4.8
5.9
5.1
Petal length (in cm) of Iris setosa:
x2; n2 = 38
1.5
1.9
1.4
1.5
1.5...

Independent random samples of professional football and
basketball players gave the following information. Assume that the
weight distributions are mound-shaped and symmetric.
Weights (in lb) of pro football players:
x1; n1 = 21
245
262
254
251
244
276
240
265
257
252
282
256
250
264
270
275
245
275
253
265
271
Weights (in lb) of pro basketball players:
x2; n2 = 19
202
200
220
210
192
215
223
216
228
207
225
208
195
191
207...

Independent random samples of professional football and
basketball players gave the following information. Assume that the
weight distributions are mound-shaped and symmetric.
Weights (in lb) of pro football players:
x1; n1 = 21
245
263
256
251
244
276
240
265
257
252
282
256
250
264
270
275
245
275
253
265
271
Weights (in lb) of pro basketball players:
x2; n2 = 19
202
200
220
210
193
215
223
216
228
207
225
208
195
191
207...

Independent random samples of professional football and
basketball players gave the following information. Assume that the
weight distributions are mound-shaped and symmetric.
Weights (in lb) of pro football players:
x1; n1 = 21
248
263
256
251
244
276
240
265
257
252
282
256
250
264
270
275
245
275
253
265
271
Weights (in lb) of pro basketball players:
x2; n2 = 19
204
200
220
210
192
215
223
216
228
207
225
208
195
191
207...

Independent random samples of professional football and
basketball players gave the following information. Assume that the
weight distributions are mound-shaped and symmetric.
Weights (in lb) of pro football players: x1; n1 = 21 246 261 255
251 244 276 240 265 257 252 282 256 250 264 270 275 245 275 253 265
271
Weights (in lb) of pro basketball players: x2; n2 = 19 203 200
220 210 192 215 223 216 228 207 225 208 195 191 207...

The following results come from two independent random samples
taken of two populations.
Sample 1
Sample 2
n1 = 60
n2 = 35
x1 = 13.6
x2 = 11.6
σ1 = 2.3
σ2 = 3
(a)
What is the point estimate of the difference between the two
population means? (Use
x1 − x2.)
(b)
Provide a 90% confidence interval for the difference between the
two population means. (Use
x1 − x2.
Round your answers to two decimal places.)
to
(c)...

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...

Consider the data to the right from two independent samples.
Construct 95% confidence interval to estimate the difference in
population means. Click here to view page 1 of the standard normal
table. LOADING... Click here to view page 2 of the standard normal
table.
x1= 44
x2=50
σ1=10
σ2=15
n1= 32
n2 = 39 The confidence interval is what two numbers, . (Round
to two decimal places as needed)

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