Practice Test 11

A school district surveyed a simple random sample of 400 high school students about whether they get at least 8 hours of sleep on a typical school night. In the sample, 172 students said “yes.” A 95% confidence interval for the true proportion $p$ of all high school students in the district who get at least 8 hours of sleep is $(0.39,\ 0.47)$. Which interpretation is correct?

A nutritionist studies whether daily fiber intake ($x$, grams) predicts LDL cholesterol ($y$, mg/dL) using a random sample of 35 adults. The regression of LDL on fiber is fit, and a slope test is conducted: $H_0: \beta_1=0$ vs. $H_a: \beta_1\neq 0$. The two-sided p-value is 0.20, so at $\alpha=0.05$ the nutritionist fails to reject $H_0$. What conclusion is appropriate?