need part G ONLY,,, SOLUTION OF REST OF THE PARTS IS IN THIS LINK https://www.ch

Question

need part G ONLY,,, SOLUTION OF REST OF THE PARTS IS IN THIS LINK

https://www.chegg.com/homework-help/questions-and-answers/2-battery-pack-used-medical-device-needs-recharged-every-5-hours-random-sample-60-battery--q26890280

2. A battery pack used in a medical device needs to be recharged about every 5 hours. A random sample of 60 battery packs is selected and subjected to a life test. The average life of these batteries is 5.05 hours. Assume that battery life is normally distributed with standard deviation 0.3 hours. Is there evidence to support the claim that mean battery life is less than 4 hours? Use = 0.01 a. Write the appropriate hypothesis b. Use P-value approach to test the hypothesis. c. Use z-test to test the hypothesis. d. Use confidence interval to test the hypothesis. e. What is your conclusion? f. If the true mean life is 4.5 hours, what is the type II error? g. If the true mean life is 4.5 hours, what is the minimum sample size needed to recognize it with 95% probability

Explanation / Answer

Here as we know the we can reject the null hypothesis if and if only when sample mean

x > 4.00 + Z0.01,60 * ( / (n)

x > 4.00 + 2.3264 * (0.3/ n)

x > 4.00 + 0.698 /n

x > 4 + 0.698/n

So if we take sample size = n

Pr(x > 4 + 0.698/n ; 4.5 ; 0.3/ n ] = 0.95

1 - Pr(x < 4 + 0.698/n ; 4.5 ; 0.3/ n) = 0.05

Here Z = -1.645

(4 + 0.698/n - 4.5) /(0.3/n) = -1.645

0.698/n - 0.5 = - 0.4935/n

1.192/n = 0.5

n = 2.383

n = 5.68

n = 6

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