Use the given information to find the $P$-value. Also, use a $0.05$ significance level and state the conclusion about the null hypothesis (reject the null hypothesis or fail to reject the null hypothesis). With $H _ { 1 } : p \neq 3 / 5$, the test statistic is $z = 0.78$.
A) $0.4354$; reject the null hypothesis
B) $0.4354$; fail to reject the null hypothesis
C) $0.2177$; reject the null hypothesis
D) $0.2177$ fail to reject the null hypothesis

Question

Quizplus · Accepted Answer

To find the P-value, we need to find the probability of getting a test statistic as extreme as or more extreme than the one we have (in either direction) if the null hypothesis is true.

Since it is a two-tailed test (the alternative hypothesis is "not equal to"), we need to find the area in both tails beyond the test statistic. Using a standard normal distribution table or calculator, we find the area beyond 0.78 in both tails to be approximately 0.4354.

Since the P-value (0.4354) is greater than the significance level (0.05), we fail to reject the null hypothesis. We do not have evidence to support that the true population proportion is different from 3/5.

Use the Given Information to Find The PPP -Value Also, Use A to Find

Use the Given Information to Find The $P$ -Value Also, Use A to Find