Question

(a) state the appropriate null and alternate hypotheses.
$h_0: p = 0.68$
$h_1: p > 0.68$
this hypotheses test is a right - tailed test.
part 2 of 5
(b) compute the value of the test statistic. round the answer to at least two decimal places.
z = 2.01
part: 2 / 5
part 3 of 5
(c) compute the p - value. round the answer to at least four decimal places.
p - value =

Explanation:

Step1: Recall P - value for right - tailed test

For a right - tailed hypothesis test with a z - score of \(z = 2.01\), the P - value is the probability that \(Z>2.01\) where \(Z\) follows the standard normal distribution \(N(0,1)\). The formula for the P - value in a right - tailed test is \(P - value=P(Z > z)\), and since \(P(Z>z)=1 - P(Z\leq z)\), we can use the standard normal distribution table (or a calculator with a normal - distribution function) to find \(P(Z\leq2.01)\) first.

Step2: Find \(P(Z\leq2.01)\)

Looking up the value of \(z = 2.01\) in the standard normal distribution table, the cumulative probability \(P(Z\leq2.01)\) is approximately \(0.9778\).

Step3: Calculate the P - value

Using the formula \(P - value = 1-P(Z\leq z)\), substitute \(z = 2.01\) and \(P(Z\leq2.01)=0.9778\) into the formula. So \(P - value=1 - 0.9778=0.0222\).

Answer:

\(0.0222\)