Question

Consider the following hypothesis test: H 0: 20 H a: < 20 A sample of 50 provided a sample mean of 19.4. The population standard deviation is 2. a. Compute the value of the test statistic (to 2 decimals). If your answer is negative, use minus "-" sign

Answer 1

Question:

A sample of 50 provided a sample mean of 19.4. The population standard deviation is 2.

a. Compute the value of the test statistic.

b. What is the p-value?

c. Using α = .05, what is your conclusion?

d. What is the rejection rule using the critical value? What is your conclusion?

Answer:

a. The test statistic is

z = -2.1213

b. p-value = 0.0170

c. Reject H₀ as α = 0.05 > P

d. For z = 0.05 critical value = -1.64 > -2.12 Reject H₀ and accept Hₐ.

Step-by-step explanation:

H₀: μ  = 20

Hₐ: μ < 20

n = Number count of sample = 50

$\overline{\rm x}$ = Sample mean 19.4

σ = Standard deviation = 2

The test statistic is given by;

$z = \frac{\overline{\rm x} - \mu _0}{\sigma /\sqrt{n} }$

Where:

z = z statistic

Therefore,

$z = \frac{19.4 - 20}{2 /\sqrt{50} } = -2.1213$

b. Using the normal z score table, P = P(Z < -2.12) = 0.0170

c. For α = 0.05 > P ∴ Reject the null hypothesis H₀

d. The critical value is the z score value from the normal distribution table at z = 0.05 which is equal to -1.645

-2.12 < -1.645 Reject H₀ and accept Hₐ

Answer 2

The value of the test statistic is -2.121

How to determine the test statistic

The given parameters are:

Null hypothesis, H₀: μ  = 20

Alternate hypothesis, Hₐ: μ < 20

Sample size, n = 50

Sample mean, $\bar x$ = 19.4

Standard deviation, σ = 2

The test statistic is calculated as:

$z = \frac{\bar x - \mu}{\sigma/\sqrt n}$

So, we have:

$z = \frac{19.4 - 20}{2/\sqrt {50}}$

Evaluate the difference and the square root

$z = \frac{-0.6}{2/7.07}$

Evaluate the quotient

$z = -2.121$

Hence, the value of the test statistic is -2.121

Read more about test statistic at:

https://brainly.com/question/16628265