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.

​WiFi-only ​3G/4G/WiFi 48 26 35 40 44 65 52 51 60 52 48 23 38 51 56 25 36 31 50 66

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=0.05. Let μ1 be the mean battery life for​ WiFi-only tablets and μ2 be the mean battery life for​ 3G/4G/WiFi tablets.

the hypotheses is:

H0​:μ1=μ2

H1​:μ1≠μ2

Find the test statistic

tSTAT=

The critical values are=

p value=

b. Assuming that the population variances from both types of tablets are​ equal, construct and interpret a 90%, 95%, and 99​% confidence interval estimate of the difference between the population mean battery life of the two types of tablets.

Answer 1

Here in this scenario our claim is that there is difference in the mean battery life between the two types of​ tablets.

To test this claim we have to use two sample t test because here the population standard deviations is unknown. We assume that the population Variance are equal.

From the above ssmple we calculated the mean and sample Standerd deviation as below,

Further the test is performed at 0.05 level of significance as below,

The t critical value is calculated t table.

B) Now based on sample information we computed the 90%, 95% and 99% Confidence Interval for difference in means using t distribution as below,

the t critical value is calculated the t table assumed that the population Variance are equal.

Thank you.