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

47 69

21 60

31 57

30 56

42 54

45 22

26 35

31 39

60 43

52 68

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.

Answer 1

To determine if there is evidence of a difference in the mean battery life between WiFi-only and 3G/4G/WiFi tablets, we can perform a two-sample t-test assuming equal population variances.

Step-by-step explanation:

To determine if there is evidence of a difference in the mean battery life between WiFi-only and 3G/4G/WiFi tablets, we need to perform a hypothesis test. Assuming equal population variances, we can use a two-sample t-test.

Step 1: State the null and alternative hypotheses:

Null hypothesis (H0): The mean battery life of WiFi-only tablets is equal to the mean battery life of 3G/4G/WiFi tablets.

Alternative hypothesis (Ha): The mean battery life of WiFi-only tablets is different from the mean battery life of 3G/4G/WiFi tablets.

Step 2: Set the significance level (α). The question states α = 0.02.

Step 3: Calculate the test statistic and p-value. Using the given data, calculate the sample means and standard deviations for both groups. Then perform the t-test calculation to find the test statistic and p-value.

Step 4: Make a decision. Compare the p-value to the significance level. If the p-value is less than α, reject the null hypothesis. Otherwise, fail to reject the null hypothesis.