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The 95% confidence interval for a certain proportion p is from 0.23 to 0.63. We conducted a hypothesis test for p. The null hypothesis is H0:p=a . The alternative hypothesis is Ha:p≠a. What is the mean for the all possible values of a which would not be rejected as plausible values of the population proportion at a 5% significance level? The mean for the all possible values of a which would not be rejected as plausible values of the population proportion at a 5% significance level is .

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Answer:

The answer is "0.43"

Step-by-step explanation:

Population proportion normal distribution is suggested as following:

Confidence Interval = [tex]P \pm Z \times \sqrt{\frac{P \times (1 -p)}{n} }[/tex]

Confidence Interval = [tex]P \pm E[/tex]

Bottom bound [tex]= P-E = 0.23[/tex]

Lower bound [tex]= P + E = 0.63[/tex]

Through connecting additional formulas, we're getting,

[tex]\to 2P = 0.23+0.63\\\\\to 2P = 0.86\\\\\to P= \frac{0.86}{2}\\\\[/tex]

        [tex]= 0.43[/tex]

The average with all attribute outcomes a whereby the demographic proportion at 5 % isn't dismissed as plausible values is 0.43.