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
49
50
25
28
31
33
39
57
47 57
Compact 70 30 60 35 55 39 59 46 52 68

. 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

alpha equals 0.05α=0.05.

▼

Do not reject

Reject

Upper H 0H0.

There is

▼

insufficient

sufficient

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 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.

B.

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.

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

A.

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

B.

The probability of a Type II error is​ 5%

C.

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

D.

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

Answer 1

First we need to find the mean and SD of all data sets. Following is the output of descriptive statistics:

Descriptive statistics
	Subcompact	Compact
count	10	10
mean	41.60	51.40
sample standard deviation	11.94	13.65
sample variance	142.49	186.27
minimum	25	30
maximum	57	70
range	32	40

Let population 1: Subcompact

Population 2: Compact

Here we have 41.6, -11.94, n-10 2-51.4, S2 13.65, n2-10 Hypotheses are Test is two tailed. Level of significance : α-0.05 Since we can assume that variances are equal so degree of freedom of t test will be The pooled standard deviation is: -12.8235 nm +n2-2 Test Statistics ((41.6-51.4)-0)/(12.8235 sqr1/10)+ (1/10))) n21.709 Critical value: 2.101 Rejection Region: If t| >2.101, Reject HO Decision: Since test statistics does not lie in rejection region so we fail to reject the null hypothesis P-value: P-value-0.1046 Decision: Since p-value is not less than level of significance so we fail to reject the null hypothesis Excel function for critical value: ะโ1NV(0.05, 18) Excel function for p-value: DIST( 1.709, 18,2)

Correct options:

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