Question

A cell phone manufacturer claims that the population mean battery life of its flagship smartphone model, the Black Bear, is greater than the population mean battery life of the largest competitor, the Grizzly. A consumer advocacy publication tests this claim by purchasing a random sample of Black Bear smartphones and a random sample of Grizzly smartphones. Members of the publication charged each smartphone to full capacity and then had the smartphones play back the same videos until the batteries were completely depleted. The publication researched the population standard deviation of the battery life from the manufacturers. The population standard deviation for the Black Bear is assumed to be 0.71 hour, and the population standard deviation for the Grizzly is assumed to be 0.63 hour. The results of the battery life test are shown below. Let μ1 be the population mean battery life for the Black Bear and μ2 be the population mean battery life for the Grizzly. If the test statistic is z=1.38, what is the p-value for this hypothesis test?

Do not round your answer; compute your answer using a value from the table below.

z	0.00	0.01	0.02	0.03	0.04	0.05	0.06	0.07	0.08	0.09
0.6	0.726	0.729	0.732	0.736	0.739	0.742	0.745	0.749	0.752	0.755
0.7	0.758	0.761	0.764	0.767	0.770	0.773	0.776	0.779	0.782	0.785
0.8	0.788	0.791	0.794	0.797	0.800	0.802	0.805	0.808	0.811	0.813
0.9	0.816	0.819	0.821	0.824	0.826	0.829	0.831	0.834	0.836	0.839
1.0	0.841	0.844	0.846	0.848	0.851	0.853	0.855	0.858	0.860	0.862
1.1	0.864	0.867	0.869	0.871	0.873	0.875	0.877	0.879	0.881	0.883
1.2	0.885	0.887	0.889	0.891	0.893	0.894	0.896	0.898	0.900	0.901
1.3	0.903	0.905	0.907	0.908	0.910	0.911	0.913	0.915	0.916	0.918

Answer 1

be the population mean battery life for the Black Bear

be the population mean battery life for the Grizzly

claim: the population mean battery life of its flagship smartphone model, the Black Bear, is greater than the population mean battery life of the largest competitor, the Grizzly.

Null hypothesis : H_o : = ; - = 0

Alternate Hypothesis :H_a   > ; - >  0

Right Tailed test;

test statistic is z=1.38

For Right tailed test :

From the given tables, P(Z 1.38) = 0.916

P(Z>1.38) = 1-P(Z 1.38) = 1-0.916=0.084

p-value for this hypothesis test = 0.084