A machine is set to produce disc plates with a mean diameter of 14 mm. A sample of 8 discsgave a mean diameter, ?̅ = 14.9 mm and a standard deviation, s = 1.33mm. A test wascarried out at the 5% level of significance to determine whether the machine is in goodworking order. Assume that the diameter of the disc follows a normal distribution. i. State, in symbols, the null and alternate hypotheses for this test.  ii. State, with reasons, whether a t-test or a z-test will be appropriate.  iii. (Determine the rejection region(s) of the test.  iv. Calculate the value of the test statistic.  v. State, with reason, a valid conclusion for the test.

For the NM March rainfall in inches: How many months (of March for NM rainfall) would need to be selected in a new sample to achieve a standard error of no more than 0.125 inches?  Note: For the twenty months NM March rainfall the sample mean was 1.4805 inches and the sample standard deviation is 0.97123 inches.

The Weather Underground reported that the mean amount of summer rainfall for the northeastern US is at least 11.52 inches. Ten cities in the northeast are randomly selected and the mean rainfall amount is calculated to be 7.73 inches with a standard deviation of 1.3 inches. At the  ? = 0.05  level, can it be concluded that the mean rainfall was below the reported average? Assume the amount of summer rainfall follows a normal distribution. a)State alpha. (Enter an exact number as an integer, fraction, or decimal.)

Has the number of shoppers who wear masks changed from 2020 to 2021? There are arguments for and against this question. The mean number of masks, u, used by a shopper in Metropolis in 2020 will be compared to the mean number of masks, Hy used by a shopper in Metropolis in 2021. The true values of u, and u, are unknown. It is recognized that the true standard deviations are o, = 19 for the 2020 measurements and o, = 24 for the 2021 measurements. We take a random sample of m = 255 shoppers in 2020 and a random sample of n = 200 shoppers in 2021. The mean number of masks were x= 97 for 2020 and y= 85 for 2021. Assuming independence between the years and assuming masks used by shoppers are normally distributed we would like to estimate x - Hy. What is the standard deviation of the distribution of x? What is the standard deviation of the distribution of x - y? Create a 95% confidence interval for uy - Hy ? ) What is the length of the confidence interval in part c) ? If we let n stay at 200…