Question

The following is a set of hypotheses, some information from one or more samples, and a standard error from a randomization distribution. Test H0 : p=0.28 vs Ha : p<0.28 when the sample has n=800, and p^=0.217 with SE=0.01. Find the value of the standardized z-test statistic. Round your answer to two decimal places.

Answer 1

Answer:

The standardized z-test statistic value is -6.3

Explanation:

Data provided in the question:

For Test H₀:

p = 0.28

n = 800

$\hat p$ = 0.217

Standard error, SE = 0.01

Now the value of the standardized z-test statistic is calculated using the formula ;

$z = \frac{\hat{p}\ -\ p}{SE}$

On substituting the respective values, we get

$z = \frac{0.217\ -\ 0.28}{0.01}$

or

z = -6.3

Hence,

The standardized z-test statistic value is -6.3

Answer 2

The value of the standardized z-test statistic is equal to -6.3.

Given the following data:

• Sample mean = 0.217.

• Standard error (SE) = 0.01.

• Sample size = 800.

How to calculate the standardized z-test statistic.

For the null hypothesis, we would test that:

$H_o : p =0.28$

For the alternate hypothesis, we would test that:

$H_a < p =0.28$

What is a z-score?

A z-score is also referred to as a standard score and it can be defined as a measure of the distance between a data point (raw score) and the mean, when standard deviation units are used.

Mathematically, the standardized z-test statistics would be calculated by using this formula:

$Z_o=\frac{\bar{p}\;-\;0.28}{ SE }\\\\Z_o=\frac{0.217\;-\;0.28}{0.01 }\\\\Z_o=\frac{-0.063}{0.01 }$

Zo = -6.3.

Read more on z-scores here: https://brainly.com/question/4302527