The following table shows the results of two random samples that measured the av

Question

The following table shows the results of two random samples that measured the average number of minutes per charge for AA Lithium-ion (Li-ion) rechargeable batteries versus Nickel-Metal Hydride (NiMH) rechargeable batteries. Complete parts a through c.

PLEASE SHOW ALL WORK

                                                    Li-ion                         NiMH

Sample mean                                  96.7                          82.5

Sample standard deviation              6.8                            11.3

Sample size                                      15                             19

Calculate the appropriate test statistic and interpret the result.

The test statistic is

(Round to two decimal places as needed.)

The critical value(s) is(are) .

(Round to two decimal places as needed. Use a comma to separate answers as needed.)

b. Identify the p-value from part a and interpret the result.

The p-value is

(Round to three decimal places as needed.)

Explanation / Answer

a)

H0: 1 - 2 = 0 i.e. (1 = 2)

H1: 1 - 2 0 i.e. (1 2)

Assuming population variances are equal, we would have to calculate pooled-variance t-Test keeping Li-ion as population 1 and NiMH as population 2

Sp^2= (n1-1)S1^2+(n2-1)S2^2/(n1-1)+(n2-1)

         = (15-1)*6.8^2+(19-1)*11.3^2/14+18

         = 647.36+2298.42/32

         = 2945.78/32

         = 92.055625

tSTAT=(X1-X2)-(µ1-µ2)/Sp^2(1/n1+1/n2)

       =(96.7-82.5)-0/92.055625(1/15+1/19)

       =14.2/3.3139

       =4.2849

tCRIT at a=0.05 is +/- 2.0369 and hence reject the null hypothesis

b)

The P-Value is 0.000156.

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