Answer:
The degrees of freedom are given by:
The p value for this case would be given by:
Since the p value is higher than the significance level we have enough evidence to FAIl to reject the null hypothesis and we can conclude that the true mean is not significantly different between the two types of battery
Step-by-step explanation:
Information given
Battery 1 106 111 109 105
Battery 2 125 103 121 118
We can calculate the mean and the deviation with the following formulas"
represent the mean for the Battery 1
represent the mean for the Bettery 2
represent the sample standard deviation for the Battery 1
represent the sample standard deviation for the battery 2
sample size selected for the Battery 1
sample size selected for the Battery 2
represent the significance level
t would represent the statistic
represent the p value
System of hypothesis
We want to check if the difference in longevity between the two batteries, the system of hypothesis would be:
Null hypothesis:
Alternative hypothesis:
The statistic is given by:
(1)
The statistic is given by:
The degrees of freedom are given by:
The p value for this case would be given by:
Since the p value is higher than the significance level we have enough evidence to FAIl to reject the null hypothesis and we can conclude that the true mean is not significantly different between the two types of battery