What test statistic would you use for the following hypothesis test (z statistic

Question

What test statistic would you use for the following hypothesis test (z statistic or t statistic)? Why? What else did I missing in this chart? Also, plz answer these four questions and show the work.

What would it mean to commit a type 1 error?

What would it mean to commit a type 2 error?

How will you know if you commit a type 1 error or not?

What is the likelihood of committing a type 1 error?

Sample 20 customers to see if they lead you to believe the proportion of customers in your population with a positive view of your company is More than 60%. Sample 20 customers to see if they lead you to believe that average age of your customer is More than 25 years of age. Sample 20 customers to see if they lead you to believe the average income of your customers is $50,000. Assume a population standard deviation of $5,000. Sample 20 of your customers to see if they lead you to believe that less than 30% of your customers have an income of less than $25,000 a year. Sample 20 of your customers to see if they lead you to believe the average number of purchases per year among your customers is less than 18

Explanation / Answer

Answers

1. All the test statistics mentioned in the chart are appropriate for the respective cases.

2. But, in all cases, the null hypothesis is wrongly stated. A null hypothesis is ALWAYS of the equality form. So, the correct null hypotheses for the above cases, in the given order, would be:

Pi = 0.6, Pop mean = 25, Pop mean = 50000, Pi = 0.3, Pop mean = 18.

3. The alternative specified in all the cases are correct.

4. On what is missing, the exact statistics formula could be given; specify the level of significance and clearly indicate the rejection criterion, such as ‘reject H0 if calculated value of the test statistics is greater than the ….% point of ….. distribution.

Type 1 error refers to the error of rejecting the null hypothesis when it is in reality true. For example, in the above first case, it would be rejecting the Pi is 0.6 when actually Pi is equal to 0.6.

Type 2 error is committed when we accept a null hypothesis when in reality it is not true, i.e., accepting H0 when HA is true.

The following explanation answers the next two queries, “How will you know if you commit a type 1 error or not?” and “What is the likelihood of committing a type 1 error?” together.

Since it is not possible to derive any test which has neither Type I error nor Type II error, all tests are derived by fixing a certain probability of committing Type I error and then selecting out of such tests, a test which has minimum probability of committing Type II error. The pre-fixed probability of committing Type I error is called ‘level of significance’. Thus, when we say that level of significance for a test is 5%. we are implying that by using that test, there is 5% chance of Type I error.

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