91影视

The parameter of interest is the population value, for which the value or other information is required. PARAMETER OF INTEREST = Population proportion$p$ of all students willing to report other students' cheating.

$$\begin{gathered} n=172 \\ p=0.15 \end{gathered}$$

Random, Normal, and Independent conditions for performing a one-sample$z$test.

Random: satisfied because the sample is a simple random sample.

Normal: If the number of failures $n(1-p)$and the number of successes $np$are both greater than$10$, the distribution is assumed to be normal.

$$\begin{gathered} np=172脳0.15 \\ =25.8 \end{gathered}$$

$$\begin{gathered} n(1-p)=172脳(1-0.15) \\ =146.2 \end{gathered}$$

Both are greater than$10,$indicating that the normal requirement has been met.

Because the sample size$172$is less than$10\%$of the population size, independence can be assumed.

Therefore, all conditions are satisfied.

The P-value is displayed in the output as:

$P=0.146=14.6\%$

The probability of receiving a sample with a more extreme proportion than the given sample proportion is $0.146$ or $14.6\%$

$$\begin{gathered} H_0:p=0.15 \\ {H}_1:pnotequalto0.15 \end{gathered}$$

The confidence level reduces the significance level to $1$:

$$\begin{gathered} 伪=1-95\% \\ =1-0.95 \\ =0.05 \end{gathered}$$

P-value is given in the output:

$P=0.146$

If the P-value is less than the significance level, the null hypothesis should be rejected.

$P=0.146>0.05鈬�\text{Fail to reject}{H}_0$

There is insufficient evidence to support the claim.