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
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 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=0.02.

Do not reject or 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 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 not rejecting the null hypothesis when the null is false

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

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

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

Answer 1

a)

	Subcompact	Compact
sample mean x =	41.30	48.30
standard deviation s=	10.80	13.21
sample size n=	10	10
Pooled Variance Sp2=((n1-1)s21+(n2-1)*s22)/(n1+n2-2)=			145.567

Point estimate : x1-x2=		-7.0000
std. error se =Sp*√(1/n1+1/n2)=		5.3957
test stat t =(x1-x2-Δo)/Se=		-1.2970
p value : =		0.2110	from excel: tdist(1.297,18,2)

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

b)

p value =0.21

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)

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