Question

# An important feature of digital cameras is battery​ life, the number of shots that can be...

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.

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.

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