Question

ikes is making mugs in his ceramics class Milks' teacher claims that the average sine of amng Milcs makes is bigger than 16 oz. In a random sample of 25 mgs that Miles has made, the sample mean ua 19 and the sample standard deviation was 2 o (a) 3 points Write out the hypotheses for this test and defise the paramveters) (b) 3 points Calculate the standardized test statistic (e) 3 points What distribution should this test statistic be compared to? Be specfic (d) 3 points What tail(s) should we look in to find the p-value? ) 3 points State what your conclusion would be in as congikeyoupa 06 was 0.045 using an alpha level of 0.05. (t) 3 points State what your conclusion would be in a complete sestence if your p-value was 0.54 using an alpha level of 0.05

Answer 1

$(a)~Let,~\mu=True~average~size\\ Null~hypothesis,~H_0:\mu=16~vs.~Alternative~hypothesis,~H_a:\mu>16.\\ (b)~Test~statistic=t=\frac{\sqrt{25}(19-16)}{2}=7.5\\ (c)~Under~H_0,~Test~statistic=\frac{\sqrt{n}(\bar{x}-16)}{s}\sim t-distribution~with~df~24,\\ where,~\bar{x}=sample~mean,~s=sample~sd.\\ (d)~p-value=P(t>7.5|t\sim t_{24})=0.0000\\ (e)~Since~p-value<0.05~so~we~reject~Null~hypothesis.\\ (f)~Since~p-value>0.05,~so~we~fail~to~reject~Null~hypothesis.$