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.