Question

An important feature of digital cameras is battery life, the number of shots that can be taken before the battery needs to be recharged. The accompanying data contains battery life information for

2929

subcompact cameras and

1616

compact cameras. Complete parts (a) through (d) below.

DATA: Subcompact |
Compact |
||

298 |
395 |
||

314 |
451 |
||

287 |
452 |
||

278 |
263 |
||

250 |
352 |
||

197 |
242 |
||

335 |
332 |
||

240 |
219 |
||

27279 |
231 |
||

238 |
259 |
||

197 |
282 |
||

217 |
398 |
||

277 |
507 |
||

209 |
198 |
||

260 |
149 |
||

219 |
131 |
||

238 |
|||

209 |
|||

2205 |
|||

291 |
|||

161 |
|||

284 |
|||

203 |
|||

142 |
|||

228 |
|||

221 |
|||

197 |
|||

172 |
|||

149 |

**a.** Is there evidence of a difference in the
variability of the battery life between the two types of digital
cameras? (Use

alphaαequals=0.010.01.)

What are the correct null and alternative hypotheses?

A.

Upper H 0H0:

sigma Subscript subcompact Superscript 2σ2subcompactequals=sigma Subscript compact Superscript 2σ2compact

Upper H 1H1:

sigma Subscript subcompact Superscript 2σ2subcompactnot equals≠sigma Subscript compact Superscript 2σ2compact

B.

Upper H 0H0:

sigma Subscript subcompact Superscript 2σ2subcompactless than or equals≤sigma Subscript compact Superscript 2σ2compact

Upper H 1H1:

sigma Subscript subcompact Superscript 2σ2subcompactgreater than>sigma Subscript compact Superscript 2σ2compact

C.

Upper H 0H0:

sigma Subscript subcompact Superscript 2σ2subcompactnot equals≠sigma Subscript compact Superscript 2σ2compact

Upper H 1H1:

sigma Subscript subcompact Superscript 2σ2subcompactequals=sigma Subscript compact Superscript 2σ2compact

D.

Upper H 0H0:

sigma Subscript subcompact Superscript 2σ2subcompactgreater than or equals≥sigma Subscript compact Superscript 2σ2compact

Upper H 1H1:

sigma Subscript subcompact Superscript 2σ2subcompactless than<sigma Subscript compact Superscript 2σ2compact

What is the test statistic?

Upper F Subscript STATFSTATequals=nothing

(Round to two decimal places as needed.)

What is the critical value? Select the correct choice below and fill in the answer box within your choice.

(Round to two decimal places as needed.)

A.

Upper F Subscript alpha divided by 2Fα/2equals=nothing

B.

Upper F Subscript alphaFαequals=nothing

What is the correct conclusion?

A.

Reject

Upper H 0H0.

There is sufficient evidence of a difference in the variability of the battery life between the two types of digital cameras.

B.

Reject

Upper H 0H0.

There is insufficient evidence of a difference in the variability of the battery life between the two types of digital cameras.

C.

Do not reject

Upper H 0H0.

There is insufficient evidence of a difference in the variability of the battery life between the two types of digital cameras.

D.

Do not reject

Upper H 0H0.

There is sufficient evidence of a difference in the variability of the battery life between the two types of digital cameras.

**b.** Determine the p-value in (a) and interpret
its meaning.

The p-value in part (a) is

nothing.

(Round to three decimal places as needed.)

What does the p-value mean?

A.

The probability of obtaining a sample that yields a test statistic equal to or more extreme than the one in (a) is equal to the p-value if there is a difference in the two population variances.

B.

The probability of obtaining a sample that yields a test statistic equal to or less extreme than the one in (a) is equal to the p-value if there is a difference in the two population variances.

C.

The probability of obtaining a sample that yields a test statistic equal to or less extreme than the one in (a) is equal to the p-value if there is no difference in the two population variances.

D.

The probability of obtaining a sample that yields a test statistic equal to or more extreme than the one in (a) is equal to the p-value if there is no difference in the two population variances.

**c.** What assumption about the population
distribution of the two types of cameras is necessary in (a)?

A.

The populations are normally distributed.

B.

The populations have different means.

C.

The populations have equal means.

D.

The populations are the same size.

Is this assumption satisfied?

▼

Yes,

No,

because

▼

the subcompact sample is

the two samples are

the compact sample is

the compact sample mean is

▼

larger than the subcompact sample.

roughly symmetric.

right-skewed.

larger than the subcompact sample mean.

smaller than the subcompact sample mean.

smaller than the subcompact sample.

skewed in opposite directions.

left-skewed.

equal to the subcompact sample.

equal to the subcompact sample mean.

**d.** Based on the results of (a), which t test
should be used to compare the mean battery life of the two types
of cameras?

A.

The pooled-variance t test should be used, because the two populations have equal variances.

B.

The pooled-variance t test should be used, because the two populations do not have equal variances.

C.

The separate-variance t test should be used, because the two populations do not have equal variances.

D.

The separate-variance t test should be used, because the two populations have equal variances.

Answer #1

Following is the output of F test generated by excel:

(a)

The test statistics is;

(b)

The p-value is: 0.0002

Since p-value is small so we reject the null hypothesis.

(c)

A. The populations are normally distributed.

Following are the box plots:

Box plot shows that data is symmetric with no outliers.

Yes, because the two samples are roughly symmetric.

d)

C.

The separate-variance t test should be used, because the two populations do not have equal variances.

One of the important features of a camera is the battery life as
measured by the number of shots taken until the battery needs to be
recharged. The data shown in the table below contain the battery
life of 10 subcompact and 10 compact cameras. Complete parts (a)
through (c).
Subcompact
Compact
48
29
38
30
41
63
51
56
56
57
50
26
40
55
56
26
31
39
41
63
a. Assuming that the population variances from both...

One of the important features of a camera is the battery life as
measured by the number of shots taken until the battery needs to be
recharged. The data shown in the table below contain the battery
life of 10 subcompact and 10 compact cameras. Complete parts (a)
through (c).
Subcompact
Compact
48
29
38
30
41
63
51
56
56
57
50
26
40
55
56
26
31
39
41
63
a. Assuming that the population variances from both...

One of the important features of a camera is the battery life as
measured by the number of shots taken until the battery needs to be
recharged. The data shown in the table below contain the battery
life of 10 subcompact and 10 compact cameras. Complete parts (a)
through (c).
Subcompact
Compact
41
23
36
33
49
60
56
56
59
51
46
26
35
52
60
20
33
39
50
64
a. Assuming that the population variances from both...

One of the important features of a camera is the battery life as
measured by the number of shots taken until the battery needs to be
recharged. The data shown in the table below contain the battery
life of 10 subcompact and 10 compact cameras. Complete parts (a)
through (c).
Subcompact
Compact
50
30
35
35
46
61
58
58
57
57
41
24
37
53
54
20
34
37
45
62
a. Assuming that the population variances from both...

The accompanying table gives results from a study of words
spoken in a day by men and women. Assume that both samples are
independent simple random samples from populations having normal
distributions. Use a
0.050.05
significance level to test the claim that the numbers of words
spoken in a day by men vary more than the numbers of words spoken
in a day by women.
n
x overbarx
s
Men
185185
15 comma 668.715,668.7
8 comma 632.88,632.8
Women
211211
16...

Listed below are systolic blood pressure measurements (mm Hg)
taken from the right and left arms of the same woman. Assume that
the paired sample data is a simple random sample and that the
differences have a distribution that is approximately normal. Use
a
0.050.05
significance level to test for a difference between the
measurements from the two arms. What can be concluded?
Right arm
152152
148148
115115
129129
136136
Left arm
172172
168168
177177
148148
149149
In this example,...

The following table contains the number of successes and
failures for three categories of a variable. Test whether the
proportions are equal for each category at the
alpha equals 0.05α=0.05
level of significance.
Category 1Category 1
Category 2Category 2
Category 3Category 3
FailuresFailures
6565
4040
4747
SuccessesSuccesses
5151
4040
5858
LOADING...
Click the icon to view the Chi-Square table of critical
values.
State the hypotheses. Choose the correct answer below.
A.
Upper H 0H0:
The
categories of the variablecategories of...

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An important feature of modern tablets is battery life. Here, we
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Meanwhile, the Surface sample had a mean of 625 minutes and a
standard deviation of 6.03 minutes. We wish to know if the Ipad...

A survey was conducted of two types of marketers. The first type
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510510
(8686%)
of B2B and
230230
(5656%)
of B2C marketers commonly use a business social media tool. The
study also revealed that
302302
(5151%)
of B2B marketers and
250250
(6161%)
of B2C marketers commonly use a video social media tool. Suppose
the survey was...

Consider the data in the table collected from four independent
populations.
Sample
1
Sample
2
Sample
3
Sample
4
a) Calculate the total sum of squares (SST).
b) Partition the SST into its two components, the sum of
squares between (SSB) and the sum of squares within (SSW).
44
1414
2121
44
77
1111
2222
33
88
1717
2020
1111
66
1313
c) Using
alphaαequals=0.050.05,
what conclusions can be made concerning the population
means?
LOADING...
Click the icon to view...

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