Statistics- Test Statistic

Question

Given the following scenario, find the test statistic and correpsonding p-value. Be sure to show all relevant work and include calculator steps if used.

Among those that file tax returns, the IRS claims that less than one-half file them through an accountant or other tax professional. A survey of 1002 people who file tax returns showed that 48% of them file through an accountant or other tax professional.

Answer 1

Step 1:

Number of people whose file returns are 1002.

The IRS claims that less than one-half file, hence the probablilty of file tax return is 50% = 0.5.

Among 1002 people, 48 % of them file through accountant then .

Null hypothesis :

One of these statements must become the null hypothesis , and the other should be the alternate hypothesis.

The null hypothesis contains equality.

So for the above, the null hypothesis H₀ : p = 0.5.

Step 2:

Alternate hypothesis :

The statement that does not contain equality is the alternative hypothesis.

So for the above scenario, the alternate hypothesis H_a : p < 0.5.

Step 3:

Calculate the test statics.

Test Statics in terms of and p is .

.

Step 4:

Find the p-value.

From the Z-score table, Area is 0.1038.

.

Solution:

The null hypothesis H₀ : p = 0.5.

The alternate hypothesis H_a : p < 0.5.

Test Static : .

p-value : .