Question

An important feature of tablets is battery​ life, the number of hours before the battery needs to be recharged. The data shown in the table below contain the battery life of 10​ WiFi-only and 10​ 3G/4G/WiFi 9- through​ 12-inch tablets. Complete parts​ (a) through​ (c).

​WiFi-only ​3G/4G/WiFi 4444 2525 3030 3535 4242 7070 5050 5454 5050 5555 5050 2121 3535 5959 5555 2525 3535 3232 4141 6666

a. Assuming that the population variances from both types of tablets are​ equal, is there evidence of a difference in the mean battery life between the two types of​tablets? Use α=0.02.

Let μ1 be the mean battery life for​ WiFi-only tablets and μ2 be the mean battery life for​ 3G/4G/WiFi tablets. Determine the hypotheses. Choose the correct answer below.

A.

H0​:μ1≥μ2

H1​: μ1<μ2

B.

H0​:μ1=μ2

H1​:μ1≠μ2

C.

H0​:μ1≠μ2

H1​:μ1=μ2

D.

H0​:μ1≤μ2

H1​:μ1>μ2

Find the test statistic.

tSTAT=_____

​(Round to two decimal places as​ needed.)

Find the critical​ value(s). _____

​(Use a comma to separate answers as needed. Round to two decimal places as​ needed.)

Choose the correct conclusion below.

(Reject/Do not reject) H0. There is (sufficient/insufficient) evidence that the means differ.

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

​p-value=_____

​(Round to three decimal places as​ needed.)

Interpret the​ p-value. Choose the correct answer below.

The​ p-value is the probability of obtaining a sample that yields a t test statistic (greater than/farther away from 0/closer to 0/less than) than the computed test statistic if there is no difference in the mean battery life between the two types of tablets.

c. Assuming that the population variances from both types of tablet are​ equal, construct and interpret a 98​% confidence interval estimate of the difference between the population mean battery life of the two types of tablets.The confidence interval is

_____≤μ1−μ2≤_____.

​(Type an integer or decimal rounded to two decimal places as​ needed.)

Interpret the confidence interval. Choose the correct answer below.

A.One can say with 2​% confidence that the difference between the population mean battery life of the WiFi only and​ 3G/4G/WiFi tablets is larger than the upper bound.

B.One can say with 98​% confidence that the difference between the population mean battery life of WiFi only and​ 3G/4G/WiFi tablets falls outside this interval.

C.One can say with 98​% confidence that the difference between the population mean battery life of WiFi only and​ 3G/4G/WiFi tablets falls in this interval.

D.One can say with 2​% confidence that the difference between the population mean battery life of the WiFi only and​ 3G/4G/WiFi tablets is smaller than the lower bound.

Answer 1

(a)

Correct option:

B.

H0:

H1:

(b)

From the given data, the following statistics are calculated:

n1 = 10

1 = 39.6

s1=12.6509

n2 = 10

2 = 47.8

s2 = 14.5434

Test statistic is:

t = (39.6 - 47.8)/6.0955 = - 8.2/6.0955 = - 1.3452

So,

t_{STAT =}- 1.35

= 0.02

ndf = n1 + n2 - 2 = 10 + 10 - 2 = 18

From Table, critical values of t = 2.5524

So,

Critical values:

- 2.55, 2.55

Correct option:

Do not reject H0.There is insufficient evidence that the means differ.

(b)

t score = - 1.35

ndf = 18

By Technology, p - value = 0.194

So,

p - value = 0.194

Correct option:

The p - value is the probability of obtaining a sample that yields a t statistic that is greater than the computed test statistic if there is no difference in the mean battery life between the two types of tablets.

(c)

Confidence Interval:

(39.6 - 47.8) (2.5524 X 6.0955)

= - 8.2 15.5582

= (- 23.7582, 7.3582)

Confidence Interval:

- 23.76 < < 7.36

Correct option:

C.   one can say with 98% confidence that the difference between population mean life between battery of WiFi only and 3G/4G/WiFi tablets falls inside this interval.