Question

A random sample of 120 observations is selected from a binomial population with unknown probability of success p. The computed value of p^ is 0.69.

(1)    Test H0:p≤0.6 against Ha:p>0.6. Use α=0.05.

test statistic z=

critical zscore     

The decision is

A. There is not sufficient evidence to reject the null hypothesis.
B. There is sufficient evidence to reject the null hypothesis.


(2)    Test H0:p≥0.6 against Ha:p<0.6. Use α=0.01

test statistic z=

critical zscore     

The decision is

A. There is not sufficient evidence to reject the null hypothesis.
B. There is sufficient evidence to reject the null hypothesis.


(3)    Test H0:p=0.6 against Ha:p≠0.6Use α=0.05.

test statistic z=

positive critical z  score    

negative critical z score     

The decision is

A. There is sufficient evidence to reject the null hypothesis.
B. There is not sufficient evidence to reject the null hypothesis.

Answer 1

Here p^ is 0.69 and n=120

(1)    Test H0:p≤0.6 against Ha:p>0.6. Use α=0.05.

Test statistics is

The z-critical value for a right-tailed test, for a significance level of α=0.05 is

zc​=1.64

Graphically

As test statistics is in rejection region we reject the null hypothesis.

Decision is B. There is sufficient evidence to reject the null hypothesis.

2. Test H0:p≥0.6 against Ha:p<0.6. Use α=0.01

Test statistics is

The z-critical value for a left-tailed test, for a significance level of α=0.05 is

zc​=−1.64

Graphically

As test statistics is not in rejection area we fail to reject the null hypothesis

So decision is A. There is not sufficient evidence to reject the null hypothesis.

3. Test H0:p=0.6 against Ha:p≠0.6Use α=0.05.

Test statistics is

The z-critical values for a two-tailed test, for a significance level of α=0.05

zc​=−1.96 and zc​=1.96

Graphically

As test statistics is in the rejection region so we reject the null hypothesis

So Decision is A. There is sufficient evidence to reject the null hypothesis.