a publisher reports that 54% of their readers own a particular make of car. a marketing executive wants to…

a publisher reports that 54% of their readers own a particular make of car. a marketing executive wants to test the claim that the percentage is actually under the reported percentage. a random sample of 160 found that 45% of the readers owned a particular make of car. is there sufficient evidence at the 0.05 level to support the executives claim? step 4 of 7: determine the p - value of the test statistic. round your answer to four decimal places. answer how to enter your answer (opens in new window) tables keypad keyboard shortcuts previous step answers

a publisher reports that 54% of their readers own a particular make of car. a marketing executive wants to test the claim that the percentage is actually under the reported percentage. a random sample of 160 found that 45% of the readers owned a particular make of car. is there sufficient evidence at the 0.05 level to support the executives claim? step 4 of 7: determine the p - value of the test statistic. round your answer to four decimal places. answer how to enter your answer (opens in new window) tables keypad keyboard shortcuts previous step answers

Answer

Explanation:

Step1: Identify the hypothesis

$H_0:p = 0.54$, $H_1:p<0.54$.

Step2: Calculate the sample proportion

$\hat{p}=0.45$, $n = 160$.

Step3: Calculate the standard - error

$SE=\sqrt{\frac{p_0(1 - p_0)}{n}}=\sqrt{\frac{0.54\times(1 - 0.54)}{160}}=\sqrt{\frac{0.54\times0.46}{160}}\approx\sqrt{\frac{0.2484}{160}}\approx0.0395$.

Step4: Calculate the z - statistic

$z=\frac{\hat{p}-p_0}{SE}=\frac{0.45 - 0.54}{0.0395}=\frac{- 0.09}{0.0395}\approx - 2.28$.

Step5: Find the P - value

Since $H_1:p<0.54$, the P - value is $P(Z < - 2.28)$. Looking up in the standard normal table, $P(Z < - 2.28)=0.0113$.

Answer:

$0.0113$