Follow the requirement to compose a 350words essay using the given calculation.The calculation is provided below, please write a new

essay using this calculation. Which means except the calculation, every

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249.Follow the requirement to compose a 350words essay using the given calculation.

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The calculation is provided below, please write a new essay using this calculation. Which

means except the calculation, every sentences else needs to be writing on your own words.

Essay

1. Use the information below to complete the essay.

Case Study

Scenario

Land and Agua Insurance Company has a call center in Tempe, Arizona. The business

was originally established in Phoenix, Arizona in 1972 as a small business, and it has

grown with the population of the area. The insurance company specializes in bu ndling

insurance for cars, off-road vehicles, and watercraft (e.g., jet skis and boats). The

company has 150,000 clients in Arizona.

Marjorie Jones, Vice President of Operations, is concerned about customer complaints

and the amount of time representatives are taking to resolve the calls. The team must

focus on two areas from the preliminary data collection including call time and error

type by shift.

2. Answer the questions below in essay format. Your essay must include an introduction,

a body, and a conclusion. It must address all relevant parts of each question. Your

response should be a minimum of 500 words in length, and it should include both the

appropriate statistics and support for the analysis and interpretation. Make sure to cite

any source you use. Proper citation format for a source includes the name of the

author(s), the title of the work, the date of the publication, and the page number if you

directly quote the source.

Essay Questions: Hypothesis Tests

Using the Sample Hypothesis Test Data and Chi-Square Data, provide a summary report for

the vice president including the following information in an essay with a minimum of 500

words (the level of significance is .05):

Two-sample hypothesis test ? Discuss the hypothesis test assumptions and test you

used. Provide the test statistic and critical-value in your response. Evaluate the results

of the hypothesis test with the scenario. Provide recommendations for the vice

president.

Chi-square hypothesis test ? Discuss the hypothesis test assumptions and test you

used. Provide the test statistic and critical value in your response. Evaluate the results

of the hypothesis test with the scenario. Provide recommendations for the vice

president.

Sample Essay:

Introduction

Comparison of two population means is very common. Hypothesis testing uses

statistics to determine between hypotheses whether the data collected is statistically

significant or occurred by chance. A comparison between two population samples

depends on both the means and the standard deviations. Using student t distribution,

two population means with unknown population standard population and independent

sample student t distribution in the comparison can be used. This paper looks at two

types of hypothesis tests; the two-sample hypothesis test and the chi-square data test.

Two Sample Hypothesis Test

According to (Donnelly, 2015) there are steps to follow in hypothesis testing: step one is

stating the hypothesis to be tested; null and alternative hypothesis. Step two is a

selection of the significance level value which in this case is 5% level of significance.

And the third and last step is the calculation of the appropriate test statistic.

The test assumes that the data sampled are independently from a normal distribution.

The dependent samples have a relationship with each other. As (Donnelly, 2015) states,

a match-pair test compares two means or proportions. For the above case, for solving

two-sample test, we have our null hypothesis as u1=u2, and our alternative hypothesis

is u1 is not equal to u2, with u1 representing the mean call time in am shift and u2

representing the mean call time in pm shift. The formula of t-test is T= (u1-u2)/[Sp^2*

(sqrt1/n1+1/n2)], where Sp^2=(n-1) S1^2+(n2-1) S2^2/(n1+n2-2).

From this formula, we have the mean 1 being the sample mean call time in am shift.

Mean 2 the sample mean call time in pm shift, S1^2 is the sample variance call time of

am shift, S2^2 is the sample variance of call time of pm shift, n1 is the sample size of

am shift, n2 is the sample size of pm shift. With the data provided in the excel, we get

75 for the sample size of am shift, 10 for the sample mean of am shift and 2.86 for the

standard deviation of the am shift; 75 for the sample size of pm shift, 12.15 for the

sample mean of pm shift, 3.54 for the standard deviation of the pm shift. Then we can

get 3.2152 for the pooled standard deviation and 4.1 for the test statistic. Now we find

critical t (alpha, n1+n2-2) as 1.976. Since t-test is greater than t critical, we reject the

null hypothesis.

Chi-Square Data

With the Chi-Square Data, the tests seek to examine whether the frequency of the given

certain values is different from the frequency distribution expected (Sharpe, 2015). The

categorical values or the observed frequency refers to the integer values which are

countable since they are collected from the population of interest. While the expected

frequency distribution is that likely to occur randomly by chance if the null hypothesis is

true.

The Chi-Square Data assumes that the null hypothesis is all dependent and the

alternative hypothesis is not all dependent (Lowry, 2014). The Chi-Square tests with

known, observed frequency and expected frequency are easily solved using a calculator.

By entering all the data we have into the calculator, we will get the result for chi-square.

Therefore Chi-squared equals 2.637 with 7 degrees of freedom. The two-tailed P value

equals 0. 9164. By conventional criteria, this difference is not statistically significant.

Hence we accept the alternative hypothesis.

Conclusion

The vice president of the Land and Agua Insurance Company finds that there is no

difference in the two population means since from the two test hypothesis the t statistic

is higher than the t critical hence. The vice president can conclude that the call time

and the shift have no difference therefore all the clients should be served regardless of

the call time. Since from the chi-square data the alternative hypothesis was accepted,

the vice president can conclude that the call time and the shift are significantly related.

References

Donnelly, R. A. (2015). Business statistics (2nd ed.). Upper Saddle River, NJ: Pearson.

Lowry, R. (2014). Concepts and applications of inferential statistics.

Sharpe, D. (2015). Your chi-square test is statistically significant: Now what?. Practical

Assessment, Research & Evaluation, 20.

…

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