Question

A random sample of size 20 is taken, resulting in a sample mean of 16.45 and

a sample standard deviation of 3.59. Assume x is normally distributed and use

this information and α=0.5 to test the following hypotheses. (use critical

t.025,19 = ±2.093)

Ho: μ = 16

Ha: μ 16

Answer 1

In this case,

$Sample\:mean=\overline{x}=16.45$

$Sample\:standard\:deviation=s=3.59\:$

$Sample\:size=n=20$

$\:Degrees\:of\:freedom=19$

$Significance\:level=\alpha =0.05$

Step 1: $H_0:\mu=16$

$H_1:\mu\:\:\not= \:16$ $(Two$ $tailed$ $test)$

Step 2: $The\:test\:statistic\:is,\:t=\frac{\overline{x}-\mu }{\left(\frac{s}{\sqrt{n}}\right)}\:$

$t=\frac{16.45-16}{\left(\frac{3.59}{\sqrt{20}}\right)}=0.5606$

Step 3: $P-value=P\left(\left|t\right|>0.5606\right)=0.5816$

Step 4: Conclusion: Since the $P-value$ is greater than the significance level, we fail to reject $H_o$ .