Question

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 types of digital cameras are​ equal, is there evidence of a difference in the mean battery life between the two types of​ cameras? Use

α=0.05.

Do not reject OR Reject H0.

There is sufficient OR insufficient evidence that the means differ.

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

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

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

A.The probability of obtaining a sample that yields a t test statistic farther away from 0 in either direction than the computed test statistic if there is no difference in the mean battery life between the two types of digital cameras.

B.The probability of obtaining a sample that yields a t test statistic farther away from 0 in the positive direction than the computed test statistic if there is no difference in the mean battery life between the two types of digital cameras.

C.The probability of obtaining a sample that yields a t test statistic farther away from 0 in the negative direction than the computed test statistic if there is no difference in the mean battery life between the two types of digital cameras.

c. What is meant by a​ “.05” level of significance​ ?

A.we have a​ 5% chance of rejecting the null hypothesis when the null hypothesis is true

B.The probability of a Type II error is​ 5%

C.the lowest level of significance for which we do not reject the null is​ 5%

D.we have a​ 5% chance of not rejecting the null hypothesis when the null is false

Answer 1

	Subcompact	Compact
sample mean x =	40.50	48.90
standard deviation s=	10.08	14.26
sample size n=	10	10
Pooled Variance Sp2=((n1-1)s21+(n2-1)*s22)/(n1+n2-2)=			152.411

Point estimate : x1-x2=		-8.4000
std. error se =Sp*√(1/n1+1/n2)=		5.5211
test stat t =(x1-x2-Δo)/Se=		-1.5210
p value : =		0.1456	from excel: tdist(1.521,18,2)

Do not reject Ho

There is insufficient evidence that the means differ.
b)

p value =0.15

A.The probability of obtaining a sample that yields a t test statistic farther away from 0 in either direction than the computed test statistic if there is no difference in the mean battery life between the two types of digital cameras.

c)

A.we have a​ 5% chance of rejecting the null hypothesis when the null hypothesis is true