# Calculate The Test Statistic And P-Value by ClassOf1

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Sub: Statistics                                                                     Topic: Hypothesis Testing

Calculate the Test Statistic and P-Value

Question:
Calculate the test statistic and p-value for each sample. Use Appendix below to calculate the p-value.

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Sub: Statistics                                                                     Topic: Hypothesis Testing

Test Statistic             p-value

H0: π = .30 versus H1: π ≠ .30, α = .05, x = 18, n = 40

Suppose you always reject the null hypothesis, regardless of any sample evidence.

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Sub: Statistics                                                                     Topic: Hypothesis Testing
What is the probability of Type I error?

P(Type I error)

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Sub: Statistics                                                                        Topic: Hypothesis Testing

Solution:
H0: π = .30 versus H1: π ≠ .30, α = .05, x = 18, n = 40

The information in the given problem can be represented with the following notations:

Null Hypothesis: H0: P = 0.30

That is, the population proportion is equal to 0.30

Alternate Hypothesis: H1: P ≠ 0.30

That is, the population proportion is not equal to 0.30

Test Statistic:

The test statistic is:

p P
Z
P *Q
n

Thus, P = 0.30

Q = 1 – P = 1 – 0.30 = 0.70

p = X/n = 18/40 = 0.45

Therefore,

0.45 0.30
Z
0.30 * 0.70
40

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Sub: Statistics                                                                      Topic: Hypothesis Testing
0.15
=
0.00525

= 2.0702 ~ 2.07

Thus, the test statistic is 2.07

The p-value of the test statistic is calculated as follows:

P (Z > z) = 2 * (1 – P (Z < z)) = 2 * (1 – 0.9808) (by referring the Appendix C – 2)

= 0.0384

Therefore, the required p-value is 0.0384

Hypothesis                                                                                  Test statistic
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