Test the hypothesis using the Pvalue approach Be sure to ver

Test the hypothesis using the P-value approach. Be sure to verify the requirements of the test. H_0: p = 0.7 versus H_1: p > 0.7 n =-200; x = 145, alpha = 0.1 Isnp_0(1 - p_0) > 10? Use technology to find the P-value. (Round to three decimal places as needed.) the null hypothesis, because the P-value is than alpha.

Solution

here n=200 and p₀ is the value of p under H0

so p₀=0.7

hence np₀(1-p₀)=200*0.7*(1-0.7)=42>=10

hence the correct option is YES

here p is the proportion of the population.

the sample proportion is f=x/n=145/200=0.725

now E[f]=p and Var[f]=p(1-p)/n

since n=200 is very large , using central limit theorem the distribution of f can be approximated by a normal distribution.

so f~N(p,p(1-p)/n)

so T=(f-0.7)/sqrt(0.7(1-0.7)/n) follows a N(0,1) distribution under H0 since under H0 p=0.7

now observed value of T is t=(0.725-0.7)/sqrt(0.7(1-0.7)/200)=0.7715

since here the alternative hypothesis is right sided,

the P value is P[T>0.7715] where T~N(0,1)

so P[T>0.7715]=0.220205 [using technology-minitab]

so p value = 0.220

alpha=0.1

and p value>alpha

so accept/failed to reject the null hypothesis because the P value is greater than alpha