all steps for hypothesis testing and calculations. A new herbal supplement claims to improve physical fitness. A sample of n=16 average score for the sample is M=39, the distribution of test scores is normal with mu = 35 and a standard deviation of =12 use a one-tailed test with an alpha level of =.05

Question

all steps for hypothesis testing and calculations.  A new herbal supplement claims to improve physical fitness. A sample of n=16  average score for the sample is M=39, the distribution of test scores is normal with mu = 35 and a standard deviation of  =12 use a one-tailed test with an alpha level of  =.05

anonymous · Answer

1. Establish your null and alternative hypotheses. The null hypothesis takes on the given average in this case, such that $\mu_0$ (the mean) is $35$. The alternative hypothesis claims that the calculated mean, $M=39$ in this case, is greater than the mean under the null hypothesis. 2. Determine the rejection region. We're given a significance level of $\alpha=0.05$ and a sample size of $n=16$. The latter tells us that we have $15$ degrees of freedom. The critical value $t_{1-\alpha,n-1}$ is thus $t_{0.95,15}\approx1.753$ (value taken from this table: ` http://www.sjsu.edu/faculty/gerstman/StatPrimer/t-table.pdf `). This means if our computed $t$ statistic satisfies $t>1.753$, we reject the null hypothesis. 3. Compute the test statistic. $$t=\frac{M-\mu_0}{\sigma/\sqrt n}=\cdots$$ 4. State the conclusion. Is $t>1.753$ ?