Question

You wish to test the following claim ( H a ) at a significance level of α = 0.01 . H o : p = 0.2 H a : p > 0.2 You obtain a sample of size n = 123 in which there are 35 successful observations. For this test, you should use the (cumulative) binomial distribution to obtain an exact p-value. (Do not use the normal distribution as an approximation for the binomial distribution.) The p-value for this test is (assuming H o is true) the probability of observing... at most 35 successful observations at least 35 successful observations What is the p-value for this sample? (Report answer accurate to four decimal places.) p-value = The p-value is... less than (or equal to) α greater than α This test statistic leads to a decision to... reject the null accept the null fail to reject the null As such, the final conclusion is that... There is sufficient evidence to warrant rejection of the claim that the population proportion is greater than 0.2. There is not sufficient evidence to warrant rejection of the claim that the population proportion is greater than 0.2. The sample data support the claim that the population proportion is greater than 0.2. There is not sufficient sample evidence to support the claim that the population proportion is greater than 0.2.

Answer 1

answer)

Null hypothesis Ho : P = 0.2

Alternate hypothesis Ha : P > 0.2

N = 123

P = 0.2

First we need to check the conditions of normality that is if n*p and n*(1-p) both are greater than 5 or not

N*p = 24.6

N*(1-p) = 98.4

Both the conditions are met so we can use standard normal z table to estimate the P-Value

Test statistics z = (oberved p - claimed p)/standard error

Standard error = √{claimed p*(1-claimed p)/√n

Observed P = 35/123

Claimed P = 0.2

N = 123

After substitution

Z = 2.34

From z table, P(z>2.34) = 0.0096

As the obtained P-Value is less than 0.01(given significance level ) alpha

We reject the null hypothesis Ho

There is enough evidence to support the claim.that p > 0.2