Question

Consider versus A random sample of 16 observations taken from this population produced a sample mean of 75.8. The population is normally distributed with a. Calculate the p-value. Round your answer to four decimal places.

Answer 1

Answer:

The p-value is 0.0012.

Step-by-step explanation:

The hypothesis is:

H₀: µ = 72 vs. Hₐ: µ > 72

The information provided is:

$n =16\\\bar x=75.8\\\sigma=5$

Compute the test statistic value as follows:

$z=\frac{\bar x-\mu}{\sigma/\sqrt{n}}$

  $=\frac{75.8-72}{5/\sqrt{16}}\\\\=3.04$

Compute the p-value as follows:

$p-value=P(Z>3.04)\\\\=1-P(Z<3.04)\\\\=1-0.99882\\\\=0.00118\\\\\approx 0.0012$

*Use a z-table.

Thus, the p-value is 0.0012.