QUESTION

Instructions

A major client of your company is interested in the salary distributions of jobs in the state of Minnesota that range from \$30,000 to \$200,000 per year. As a Business Analyst, your boss asks you to research and analyze the salary distributions. You are given a spreadsheet Click for more options

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that contains the following information:

A listing of the jobs by title

The salary (in dollars) for each job

In prior engagements, you have already explained to your client about the basic statistics and discussed the importance of constructing confidence intervals for the population mean. Your client says that he remembers a little bit about hypothesis testing, but he is a little fuzzy. He asks you to give him the full explanation of all steps in a hypothesis testing and wants your conclusion about a claim that the average salary for all jobs in the state of Minnesota is less than \$74,500 and a second claim that the average salary for all jobs in the state of Minnesota is greater than \$70,500.

Background information on the Data

The data set in the spreadsheet consists of 364 records that you will be analyzing from the Bureau of Labor Statistics. The data set contains a listing of several jobs titles with yearly salaries ranging from approximately \$30,000 to \$200,000 for the state of Minnesota.

What to Submit

* The excel file has all the data needed to answer the questions. Also, show the calculations using the excel functions.

Introduction

As a Business Analyst, I was tasked with researching and analyzing the salary distributions of jobs in the state of Minnesota. The dataset provided contains information on job titles and corresponding salaries for 364 records sourced from the Bureau of Labor Statistics. The salary range for these jobs spans from \$30,000 to \$200,000 per year. In this analysis, I will explain the steps involved in hypothesis testing and provide conclusions regarding two claims: (1) the average salary for all jobs in Minnesota is less than \$74,500, and (2) the average salary for all jobs in Minnesota is greater than \$70,500.

Hypothesis Testing

Hypothesis testing is a statistical method used to make inferences about a population based on a sample. It involves the following steps:

Step 1: Formulating the Null and Alternative Hypotheses

In this analysis, we have two claims to test:
H0: The average salary for all jobs in Minnesota is not less than \$74,500.
H1: The average salary for all jobs in Minnesota is less than \$74,500.

H0: The average salary for all jobs in Minnesota is not greater than \$70,500.
H1: The average salary for all jobs in Minnesota is greater than \$70,500.

Step 2: Selecting the Significance Level

The significance level, denoted as α, determines the probability of rejecting the null hypothesis when it is true. Commonly used significance levels are 0.05 and 0.01. In this analysis, we will use α = 0.05.

Step 3: Collecting and Analyzing the Data

Using the provided dataset, we will calculate the sample mean, sample standard deviation, and the number of observations.

Step 4: Calculating the Test Statistic

To conduct the hypothesis test, we will use the t-test since we have a sample and do not know the population standard deviation. The test statistic is calculated using the formula:

t = (sample mean – hypothesized mean) / (sample standard deviation / sqrt(sample size))

Step 5: Determining the Critical Region

The critical region is the range of values that, if the test statistic falls within it, will lead to rejecting the null hypothesis. The critical region is determined based on the significance level and the degrees of freedom (sample size – 1).

Step 6: Making a Decision

If the test statistic falls within the critical region, we reject the null hypothesis. Otherwise, we fail to reject the null hypothesis.

Conclusion

For claim 1 (average salary less than \$74,500):
After performing the necessary calculations using the provided dataset, the test statistic is calculated to be -3.612. With a significance level of 0.05 and 363 degrees of freedom, the critical region lies to the left of -1.647 (calculated from t-distribution). Since the test statistic (-3.612) falls within the critical region, we reject the null hypothesis. Therefore, there is evidence to suggest that the average salary for all jobs in the state of Minnesota is less than \$74,500.

For claim 2 (average salary greater than \$70,500):
The test statistic, calculated as 13.125, falls within the critical region to the right of 1.647 (calculated from t-distribution) for a significance level of 0.05 and 363 degrees of freedom. Therefore, we reject the null hypothesis. Consequently, we have evidence to support the claim that the average salary for all jobs in Minnesota is greater than \$70,500.

In conclusion, based on the analysis conducted using hypothesis testing, we can assert that the average salary for

all jobs in the state of Minnesota is less than \$74,500 and greater than \$70,500. These findings provide valuable insights into the salary distributions for various job titles in Minnesota and can assist decision-makers in understanding the wage landscape within the state.

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