A consumer organization collected data on two types of automobile batteries, A and B. The summary statistics for 12 observations of each type are . X(bar)A=36.51, X(bar)B=34.21, SA=1.43, SB=.93. Assume that the data are normally distributed with OA=OB.

Is there evidence to support the claim that type A battery mean life exceeds that of type B? Test the hypothesis at alpha = 0.05

Construct a 99% Confidence interval (CI) for the difference in the mean battery life.

There evidence to support the claim that type A battery mean life exceeds that of type B.

The 99% Confidence interval (CI) for the difference in the mean battery life is (0.91, 3.69).

Step-by-step explanation:

The hypothesis can be defined as follows:

H₀:The mean life of battery A is not more than that of battery B, i.e. .

Hₐ:The mean life of battery A is more than that of battery B, i.e. .

The significance level of the test is, α = 0.05.

The test statistic is:

Compute the value of standard error as follows:

Compute the test statistic as follows:

Decision rule:

If the test statistic value is more than the critical value, , then the null hypothesis will be rejected. And vice-versa.

Compute the degrees of freedom (df) as follows:

The critical value is,

The test statistic, t = 4.67 > = 1.729.

Thus, the null hypothesis is rejected at 5% level of significance.

Conclusion:

Thus, there evidence to support the claim that type A battery mean life exceeds that of type B.

The critical value of t for a 99% confidence level and degrees of freedom 19 is:

The pooled standard deviation is:

Compute the 99% confidence interval for the difference in the mean battery life as follows:

Thus, the 99% Confidence interval (CI) for the difference in the mean battery life is (0.91, 3.69).

check above link.

graphically?   well, you graph them both, the solutions is where they both intersect each other, since there are two solutions, meaning they will meet twice, or namely the linear will run into the quadratic curve twice, and where they meet, those x,y coordinates are the solutions to the system.