Course Project - Phase 4

Jessica Seifert

Rasmussen College

January 21, 2018

1. Discuss the process of hypothesis testing.

In statistics and other subjects of learning, the hypothesis is an opinion or a claim on an issue or item which is then tested to find out if it is accurate. The statistical inference to be specific is a conjuncture on a population parameter which then gets checked to find out whether it is correct or not.

2. The eight steps of hypothesis testing

I. Null hypothesis stating

This process involves the creation of a statement that can get defined on the opposite side of the calculated guess towards the research. A good example is where a biologist thinks that using fertilizer will lead to different height for the plants. The null hypothesis, in this instance, will be that there will be no different is plant heights.

II. Alternative Hypothesis

This statement is the opposite of null hypothesis. In our example,

the alternative hypothesis will be that there will be a difference in plant heights.

III. Setting the level of significance

This process is setting the probability of the commitment of a Type 1 error which is arguably the most grievous error one can commit when conducting the exercise. The error gets denoted by α.

IV. Data collection

This part is where the data set gets collected. That implies that the data collection can either be observational or experimental exercises.

V. Test statistic

In this stage, one states what they want to test this could be the sample proportion, sample mean or a difference of the two.

VI. Decision on type of test

The test can either be one or two-tailed. One tail testing is where the error will be found on one side of the data while two-tailed testing is where the error will be on the two side extremes.

VII. Acceptance or rejection regions

This method is where the critical values of the test will be used to determine the rejection or acceptance region of the hypothesis. An appropriate level of significance is used to manage the regions.

VIII. Standardization of the test statistic

This part is where the z-test will assist in the decision making on the rejection and acceptance of the set hypothesis. The standardization helps in concluding H0 so that where p-value will be less than less than α, then Accept Ha and Reject H0.

3. Preferred method - P-Value method or Critical Value method? Why?

The critical value is the preferred method as it involves the determination of the unlikeliness or likeliness thereby determining whether the observed test statistic is extreme than the expectation of the null hypothesis was correct. It entails the comparison between the test statistic and a cutoff value known as the critical value. Where the test statistic is found to be extreme than the critical value, the null hypothesis will get rejected, and the alternative hypothesis accepted and vice versa. This method gives a clear explanation on when to accept or reject the null hypothesis.

4. Test the hypothesis for the Minnesota case.

Since σ is unknown, we thus use the t-test which is given by:

t = (Mean –u)/s/√n

Mean = 65,000

From the case scenario, the mean is u = 62,306

And the standard deviation is unknown. Hence we use the sample in scenario 1=19149

Sample size n= 364.

Definition of the hypothesis will be

H0= The average wage for all jobs in Minnesota is equal to $65,000.(μ=65000)

H1= the average salary for all jobs in Minnesota less than $65,000( μ<65000)

Hence t = (65000-62306)/(19149/√364

t = 2694/100.68

t = 2.68

At α = 0.05 with n-1 degree of freedom (364-1)=363 under one tail

t- Value v= 1.658

Since the t-computed (2.68) is greater than t-tabulated (from table=1.658), the null hypothesis will be rejection, and a conclusion made that the average salary for all job categories is lower than $65,000.

5. Null and alternative hypothesis symbolically

H0= μ=65,000

H1= μ<65,000

6. Is the test two-tailed, left-tailed or even right-tailed? Explain…

The test is left tailed since the chances for the average salary being lower than the mean are greater. This part is on the left-hand side of the normal distribution shape.

7. Which test statistic will you use for your hypothesis test; z-test or t-test? Explain.

A t-test will get used because the data gets normally distributed and that the σ is unknown therefore the need for finding the standard error to be able to standardize the average salary.

8. What is the value of the test statistic? What is the P-value?

t=2.68, p-value<0.05.

9. What is the critical Value?

From the table t (.05,263) =1.658

10. What is your decision?

The decision is to reject null hypothesis since the t-computed (2.68) is greater than the t-tabulate found from the table (1.658) at p<.05

11. The conclusion in non-technical terms

The null hypothesis got rejected because there was enough evidence to show that the average salary for all job categories is lower than $65,000.