# Statistic Responses

Response 1.) Deborah

**One-sample hypothesis test**

One sample hypothesis test is utilized when determining if the unknown population mean varies from the particular value (Whatley 2022). The data utilized in this case should be continuous and comprise a random sample from the normal population.

**Example**A hospital wants to conduct research on cholesterol among men. Initially, it had been noted that most patients are in the hospital for medication related to other issues rather than cholesterol. Besides, non-reported to have been utilizing medication for high cholesterol. In this case, one sample hypothesis test is appropriate to determine if the unknown cholesterol means of its men patients differ from the recommended level of 200mg. Hence, a random sample is collected by measuring cholesterol among men.**Two-sample hypothesis test**A two-sample is a hypothesis test used to investigate whether the unknown means for two groups vary (Gerald 2018). Hence, any research of this kind must comprise two samples. Two sample hypothesis test is usable when the data values collected are independent and collected from a random sample of two normal populations. Besides, the independent groups data should have similar variances.ExampleTwo sample hypothesis tests can be used to determine if the patients visiting a hospital have equal mean for their cholesterol levels based on gender. In this case, the hospital should collect the cholesterol measurements for a given number of men and then apply the same process for the same number of females. The sample selected should be of the same age group. The obtained data will be examined to determine the means the male and female cholesterol levels differ.

Reference

s

Gerald, B. (2018). A brief review of independent, dependent, and one-sample t-test. I*nternational Journal of Applied Mathematics and Theoretical Physics,*4(2), 50-54.

Whatley, M. (2022). Hypothesis Testing. In *Introduction to Quantitative Analysis for International Educators* (pp. 33-55). Springer, Cham.

Response 2.) Mary

**One-Sample Test**

A hairdresser’s average appointment time on certain days is greater than 20 minutes. The sample is of 10 clients during a week. The investigation should determine whether there are any inaccuracies in the sample mean and the population mean, the standard deviation is unknown. The sample size is small under 30 people, one sample hypothesis will be used.

**Two-Sample Test**

As a culinary arts instructor I train and develop a diverse group of nationalities predominantly English-speaking individuals, however, there are some whose first language is not English.

A recipe used need to be understood by all and are in English, one group of cooks is English first language and the second group is English second language. The study will determine if the mean score is different from English as a first language from that of English as a second language using the test score to measure. Variable one identifies the groups of cooks, the second group is English as a second language to determine the mean score and if it differs. The two-sample test is applied to establish a difference between the two groups’ comprehension.

Reference

Levine, D.M., Szabat, K. A., & Stephan, D. (2021). Statistic for managers using Microsoft Excel. Pearson. ISBN-13: 97880135969854

Response 3.) Michael

One-Sample Hypothesis Test

A medical office must collect payments from patients when the patient arrives for their appointment if the patient’s insurance plan requires a copayment. It is essential to collect these copayments at the point of arrival rather than waiting to send a bill to the patient on the next billing cycle because it improves revenue cycle measures, like days’ receivable outstanding, and improves cash flow.

The revenue cycle manager for a medical practice established a standard for the receptionists to collect copayments at least 95% of the time when the insurance plan requires copayments. On a quarterly basis, the manager takes a sample of transactions for each receptionist to see if they met or exceeded the standard of 95% compliance with copayment collection.

H0: Copayment Rate ? 95%

H1: Copayment Rate < 95%

The one-sample test works best in this case because the manager needs to collect data periodically to compare it to the goal (standard) to be sure the receptionists are meeting or exceeding the goal each quarter.

Two-Sample Hypothesis Test

Press Ganey provides patient satisfaction survey tools for medical practices. The survey asks several questions about a patient’s experience with their provider and the medical practice staff. One of the first questions on the survey is about the patient’s overall rating of the medical provider on a scale of one (1) to ten (10). Those responses with a rating of nine (9) or ten (10) are considered “Top Box” scores. Each month the Press Ganey report indicates the percentage of patient surveys that scored a provider with the “Top Box” score on the overall provider rating.

A medical practice administrator with two office locations must compare each site’s “Top Box” scores. Therefore, a two-sample study will allow the administrator to collect one sample from office A and a second sample from office B to compare the “Top Box” scores and determine if they are the same or different.

H0: “Top Box” Office A Average = “Top Box” Office B Average

H1: “Top Box” Office A Average ? “Top Box” Office B Average

Once the administrator collects the data for the two offices, it will be possible to determine if one office scores higher than the other. Suppose there is a significant difference between the two offices. In that case, this will allow the administrator to investigate further and determine what is different about the office with the higher “Top Box” score.

Response 4.) Eric

A one-sample t-test compares a single population to a standard value. For example, to determine whether the average lifespan of a specific town is different from the country average. Another example is a school that wants to test that the average mean GPA for grad students is 3.0. They will use one sample t-test and can get the result.

A two-test sample compares a single population before and after some experimental intervention or at two different points. For example, one measures student performance on a test before and after being taught the material. In the same example above, if the school is interested in testing, the average GPA for science and arts majors is the same. Then they would have used a two-sample test.

I would use the two-test sample instead of one. The two-sample test is most likely used to compare two process means when the data have one nominal variable and one measurement variable. It is a hypothesis test of means. Use two sample tests if the sample size is more than 30, which will provide more data information for me.