91影视

A test statistic value of $z=2.01$ is obtained, and the claim to be tested is $p鈮�0.345$.

a.

In correspondence with the given claim, the following hypotheses are set up:

Null Hypothesis: $p=0.345$

Alternative Hypothesis: $p鈮�0.345$

Since there is a not equal sign in the alternative hypothesis, the test is two-tailed.

b.

The test statistic to test the given claim is the z-value.

The z-value is equal to 2.01.

Using the standard normal table, the corresponding two-tailed p-value for z-score equal to 2.01 is equal to:

$$\begin{gathered} 2脳P\left(z<2.01\right)=2脳\left(0.0222\right) \\ =0.0444 \end{gathered}$$

Thus, the p-value is equal to 0.0444.

To depict the p-value on the normal probability graph, follow the given steps:

• Plot a horizontal axis representing the z-score. Also, label it as 鈥渮-score鈥�.
• Sketch a bell-shaped curve and draw a vertical dotted line corresponding to the value 鈥�0鈥� on the horizontal axis
• Mark the points 鈥�-2.01鈥� and 鈥�2.01鈥� on the horizontal axis and then shade the area to the left of the value 鈥�-2.01鈥� and to the right of the value 鈥�2.01鈥� with blue as shown in the figure.
• Label the two shaded regions as 鈥減-value = 0.0222鈥�.

The following plot shows the probability value (p-value) as the shaded area under the normal probability graph. Here, the sum of the two p-values corresponds to the requited two-tailed p-value (0.0444).

c.

If the p-value is less than the level of significance, the null hypothesis is rejected; otherwise, not.

Here, the level of significance is equal to 0.05, and the p-value is equal to 0.0444.

Since the p-value is less than 0.05, the null hypothesis is rejected.