Question

1. . In a survey of 1000 American adults conducted in April 2012, 430 reported having gone through an entire week without paying for anything in cash. Test at 1% significance level to see if this sample provides evidence that the proportion of all American adults going a week without paying cash is greater than 40%.

(a) Define the parameter with proper notation. State the null and alternate hypothesis.

(b) Is it one or two tailed test? Give the direction if one tailed. What is the level of significance? Give the null value.

(c) Find the best point estimate rounded to three decimal places, with proper notation.

(d) If we were to draw a 1000 samples randomization distribution, each of size 1000, what is the expected shape and center of this randomization distribution?

(e) Draw a smooth curve of the randomization distribution and shade the area that represents the p- value for this sample.

(f) Using the following randomization distribution, find the p-value corresponding to the best point estimate. Describe the strength of the evidence based on this p-value (scale is 0.0067 units between each number).

(g) Based on the p-value what is the formal conclusion? What type of error is made? Describe what that type of error means in this situation.

(h) Based on the p-value, what is the conclusion in the context of the problem? (i) Find p-value for ?̂ = 0.45.

Answer 1

1.

(a)

Parameter is defined by

We have to test for null hypothesis

against the alternative hypothesis

(b)

This is an one tailed test.

As alternative hypothesis is of greater than type, this test is a right tailed test.

Level of significance

Null value is given by

(c)

Best point estimate of p based on the given information is given by

(d)

For 1000 samples we have,

Now,

So, expected shape is normal distribution curve and center of this randomization distribution is 0.43.