Question

use the given information to find the p - value. also, use a 0.05 significance level and state the conclusion about the null hypothesis (reject the null hypothesis or fail to reject the null hypothesis).

1. the test statistic in a right - tailed test is ( z = 1.43 ).

a) 0.1528; reject the null hypothesis
b) 0.0764; reject the null hypothesis
c) 0.1528; fail to reject the null hypothesis
d) 0.0764; fail to reject the null hypothesis

1. the test statistic in a left - tailed test is ( z=-2.05 ).

a) 0.4798; fail to reject the null hypothesis
b) 0.0404; reject the null hypothesis
c) 0.0202; reject the null hypothesis
d) 0.0453 fail to reject the null hypothesis

1. the test statistic in a two - tailed test is ( z=-1.63 ).

a) 0.0516; reject the null hypothesis
b) 0.1032; fail to reject the null hypothesis
c) 0.0516; fail to reject the null hypothesis
d) 0.9484; fail to reject the null hypothesis

1. with ( h_{1}:p

eq3/5 ), the test statistic is ( z = 0.78 ).
a) 0.2177; reject the null hypothesis
b) 0.4354; reject the null hypothesis
c) 0.2177 fail to reject the null hypothesis
d) 0.4354; fail to reject the null hypothesis

1. with ( h_{1}:p > 0.554 ), the test statistic is ( z = 1.34 ).

a) 0.9099; fail to reject the null hypothesis
b) 0.0901; reject the null hypothesis
c) 0.0901; fail to reject the null hypothesis
d) 0.1802; reject the null hypothesis

Explanation:

Step1: Find P - value for right - tailed test

For a right - tailed test with \(z = 1.43\), we use the standard normal distribution table. The area to the left of \(z = 1.43\) is \(P(Z<1.43)=0.9236\). So the \(P - value=1 - P(Z < 1.43)=1 - 0.9236 = 0.0764\).
Since \(P - value=0.0764>0.05\) (significance level \(\alpha = 0.05\)), we fail to reject the null hypothesis.

Step2: Find P - value for left - tailed test

For a left - tailed test with \(z=-2.05\), using the standard normal distribution table, \(P(Z < - 2.05)=0.0202\).
Since \(P - value = 0.0202<0.05\), we reject the null hypothesis.

Step3: Find P - value for two - tailed test

For a two - tailed test with \(z=-1.63\), the area to the left of \(z=-1.63\) is \(P(Z < - 1.63)=0.0516\). The \(P - value = 2\times P(Z < - 1.63)=2\times0.0516 = 0.1032\).
Since \(P - value=0.1032>0.05\), we fail to reject the null hypothesis.

Step4: Find P - value for two - tailed test (\(H_1:p

eq\frac{3}{5}\))
For \(z = 0.78\), the area to the left of \(z = 0.78\) is \(P(Z < 0.78)=0.7823\). The \(P - value=2\times(1 - 0.7823)=2\times0.2177 = 0.4354\).
Since \(P - value=0.4354>0.05\), we fail to reject the null hypothesis.

Step5: Find P - value for right - tailed test (\(H_1:p>0.554\))

For \(z = 1.34\), the area to the left of \(z = 1.34\) is \(P(Z < 1.34)=0.9099\). The \(P - value=1 - 0.9099=0.0901\).
Since \(P - value=0.0901>0.05\), we fail to reject the null hypothesis.

Answer:

1. D. 0.0764; fail to reject the null hypothesis
2. C. 0.0202; reject the null hypothesis
3. B. 0.1032; fail to reject the null hypothesis
4. D. 0.4354; fail to reject the null hypothesis
5. C. 0.0901; fail to reject the null hypothesis