Acomputer company claims that the batteries in its laptops last 4 hours on average. a consumer report firm gathered a sample of 16 batteries and conducted tests on this claim. the sample mean was 3 hours 50 minutes, and the sample standard deviation was 20 minutes. assume that the battery time distribution as normal.

a) test if the average battery time is shorter than 4 hours at a = 0.05.

b) construct a 95% confidence interval of the mean battery time.

c) if you were to test h0: µ =240 minutes vs. h1: µ ≠ 240 minutes, what would you conclude from your result in part (b)?

d) suppose that a further study establishes that, in fact, e population mean is 4 hours. did the test in part (c) make a correct decision? if not, what type of error did it make? 7. a computer company claims that the batteries in its laptops last 4 hours on average. a consumer report firm gathered a sample of 16 batteries and conducted tests on this claim. the sample mean was 3 hours 50 minutes, and the sample standard deviation was 20 minutes. assume that the battery time distribution as normal.

a) We can reject the null hypothesis and conclude that average battery time is shorter than 4 hours at a = 0.05

b) 95% confidence interval of the mean battery time is 230±11.55. That is between 218.45 min and 241.55 min.

c) If you were to test H0: µ =240 minutes vs. H1: µ ≠ 240 minutes, we can conclude that we fail to reject the null hypothesis, because confidence interval includes 240 min.

d) We made a correct decision at c, if study establishes that in fact, a population mean is 4 hours.

Step-by-step explanation:

a)

H0: µ=240

H1: µ<240

Test statistic can be found using the equation

where

= -2

One tailed p-value of t=-2 for  15 degrees of freedom is ≈ 0.032

Since 0.032<0.05, the result is significant. We can reject the null hypothesis and conclude that average battery time is shorter than 4 hours at a = 0.05

b) 95% confidence interval of the mean battery time can be calculated using M±where

230±  that is 230±11.55

c) If you were to test H0: µ =240 minutes vs. H1: µ ≠ 240 minutes, from 95% confidence interval which is between 218.45 min and 241.55 min, we can conclude that we fail to reject the null hypothesis, because confidence interval includes 240 min.

d) We made a correct decision at c, if study establishes that in fact, a population mean is 4 hours.

A. The average battery time is shorter than 4 hours at 0.05 level of significance and 15 degrees of freedom

B. The mean battery time is likely to be between 219.35 and 240.65 minutes at 95% confidence interval.

C. The average batter time is equal to 4 hours at 0.05 level of significance and 1 degrees of freedom

D. The test in part C made a correct decision

Step-by-step explanation: Please find the attached document for the step by step working and explanation

the correct answer is 5 6 and 7