Question

question 17
6 pts
80 out of 150 people preferred a particular pc. the null hypothesis = 0.40. using a 95% confidence;
what is the z - test calculated or critical value? round to 3 decimal places.
3.254
2.753
3.273
3.200
question 18
6 pts
80 out of 150 people preferred a particular pc. the null hypothesis = 0.40. using a 95% confidence with a two - tail z - table value to the critical value, should we reject the null hypothesis?
true
false

Explanation:

Step1: Calculate sample proportion

$\hat{p}=\frac{80}{150}\approx0.533$

Step2: Identify values for $z - test$ formula

$p_0 = 0.40$, $n=150$
The formula for the $z - test$ statistic in a proportion test is $z=\frac{\hat{p}-p_0}{\sqrt{\frac{p_0(1 - p_0)}{n}}}$

Step3: Substitute values into formula

$z=\frac{0.533 - 0.40}{\sqrt{\frac{0.40\times(1 - 0.40)}{150}}}$
First, calculate the denominator: $\sqrt{\frac{0.40\times0.60}{150}}=\sqrt{\frac{0.24}{150}}\approx\sqrt{0.0016}= 0.04$
Then, calculate the numerator: $0.533 - 0.40 = 0.133$
$z=\frac{0.133}{0.04}=3.325\approx3.325$ (rounded to 3 decimal places)

For a 95% confidence two - tail test, the critical values are $z=\pm1.96$. Since the calculated $z = 3.325>1.96$, we reject the null hypothesis.

Answer:

Question 17: 3.325
Question 18: True