Suppose the lifetime (in hours) of a battery brand is normally distributed. A random sample of 19 batteries results in a sample variance 4.75 hours2. We want to test if there is significant/sufficient evidence in the data to claim that the variance of the battery life population is different than 8 hours2 at 𝛼=0.1, which of the following is INCORRECT?

A random sample of 15 batteries resulted in an average life of 280 hours with a standard deviation of 24 hours. Assume the battery life to be normally distributed and α = 0.05. Test the following hypothesis:H0: µ = 300 hoursH1: µ ≠ 300 hoursa.reject H0.b.There is no reason to believe that the battery life has changed.c.Accept the null hypothesis.d.Fail to reject the H0.

A consumer products company is formulating a new shampoo and interested in studying the mean foam height (in mm). Assume the foam height approximately follows a normal distribution with known variance of  σ2 = 400 mm2. A random sample of 9 such new shampoos results in a mean foam height 165 mm. Test if there is sufficient evidence to support the claim that the mean foam height of the new shampoo is different from 160.5 mm at α = 0.05. Which of the following statements is INCORRECT?

The quality-control manager at a compact fluorescent light bulb(CFL)factory needs to determine whether the mean life of a large shipment of CFLs is equal to 7450 hours.The population standard deviation is 990 hours.A random sample of 81 light bulbs indicates a sample mean life of 7,252 hours. At the 0.05 level of significance.is there evidence that the mean life is different from 7450 hours? What is the test​ statistic?

A study was conducted to estimate μ, the mean number of weekly hours that U.S. adults use computers at home. Suppose a random sample of 81 U.S. adults gives a mean weekly computer usage time of 8.5 hours and that from prior studies, the population standard deviation is assumed to be σ = 3.6 hours.A similar study conducted a year earlier estimated that μ, the mean number of weekly hours that U.S. adults use computers at home, was 8 hours. We would like to test (at the usual significance level of 5%) whether the current study provides significant evidence that this mean has changed since the previous year.Using a 95% confidence interval of (7.7, 9.3), which of the following is an appropriate conclusion? The current study does provide significant evidence that the mean number of weekly hours has changed over the past year, since 8 falls outside the confidence interval. The current study does not provide significant evidence that the mean number of weekly hours has changed over the past year, since 8 falls outside the confidence interval. The current study does provide significant evidence that the mean number of weekly hours has changed over the past year, since 8 falls inside the confidence interval. The current study does not provide significant evidence that the mean number of weekly hours has changed over the past year, since 8 falls inside the confidence interval. You cannot draw a conclusion because the only way to reach a conclusion is to find the p-value of the test.

Creators of a new software claim that it measures the remaining notebook battery life with a standard deviation as low as 5 minutes. To test this claim, a fully charged notebook was disconnected from the power supply and continued on its battery. The experiment was repeated 50 times, and every time the predicted battery life was recorded. The sample standard deviation of these 50 normally distributed measurements was equal 5.7 minutes. At the 5% level of significance, do these data provide evidence that the actual standard deviation is greater than 5 min?