What is the null and alternative hypothesis? Test Statistic?

A company would like to show that the average moisture content is less than 0.35 pounds per 100 sq. feet. A random sample of 36 measurements of moisture content has an average moisture content of .325 pounds per 100 square feet with a standard deviation of .0579 pounds per 100 square feet.





I need the null and alt hypothesis, and the test statistic with the P-value|||Hypothesis Test for mean:





Assuming you have a large enough sample such that the central limit theorem holds, or you have a sample of any size from a normal population with known population standard deviation, then to test the null hypothesis


H0: 渭 鈮?螖 or


H0: 渭 鈮?螖 or


H0: 渭 = 螖


Find the test statistic z = (xbar - 螖 ) / (sx / 鈭?(n))





where xbar is the sample average


sx is the sample standard deviation, if you know the population standard deviation, 蟽 , then replace sx with 蟽 in the equation for the test statistic.


n is the sample size





The p-value of the test is the area under the normal curve that is in agreement with the alternate hypothesis.





H1: 渭 %26gt; 螖; p-value is the area to the right of z


H1: 渭 %26lt; 螖; p-value is the area to the left of z


H1: 渭 鈮?螖; p-value is the area in the tails greater than |z|





If the p-value is less than or equal to the significance level 伪, i.e., p-value 鈮?伪, then we reject the null hypothesis and conclude the alternate hypothesis is true.





If the p-value is greater than the significance level, i.e., p-value %26gt; 伪, then we fail to reject the null hypothesis and conclude that the null is plausible. Note that we can conclude the alternate is true, but we cannot conclude the null is true, only that it is plausible.





The hypothesis test in this question is:





H0: 渭 鈮?0.35 vs. H1: 渭 %26lt; 0.35





The test statistic is:


z = ( 0.325 - 0.35 ) / ( 0.0579 / 鈭?( 36 ))


z = -2.590674





The p-value = P( Z %26lt; z )


= P( Z %26lt; -2.590674 )


= 0.004789415





Since the p-value is very small we reject the null hypothesis and conclude the alternate hypothesis 渭 %26lt; 0.35 is true.|||The alt hypothesis is given directly in the problem. The null hypothesis is exactly the opposite.





Using the standard deviation and sample size, calculate the standard error (aka, the standard deviation of the sample distribution). The test statistic is the number of standard errors between the sample mean and the hypothesized population mean -- i.e. 'Z'





Look up the area corresponding to Z in a standard normal calculator to determine 'p'