Hypothesis Testing Case Solution And Analysis, HBR Case Study Solution & Analysis of Harvard Case Studies

Q1) What hypothesis testing procedure would you use in the following situations?

a) A test classifies applicants as accepted or rejected. On the basis of data on 200 applicants, we test the hypothesis that ad placement success is not related to gender.

For the situations where data is nominal and the answers are categorized as either yes or no, chi-square test would be the best and most preferable option. This test is applied in situations where the given data is grouped as nominal scale as mentioned in the question that is “accepted” or “rejected”.

b) A company manufacturers and markets automobile in two different countries. We want to know if the gas mileage is the same for vehicles from both facilities. There are samples of 45 units from each facility.

In this scenario, the company can opt for t-test and z test that will help the company in identifying two independent samples from their case study. The main difference between z test and t-test is the sample size. Sample is relatively larger in z test as compared to the sample size of t-test. On the contrary, if the population variance is known and the sample size is distributed normally then companies use z test that will be based on relatively less sample size. As in our case, the sample size is above 30 that is 45 thus; z test will be applied. However, the company can also use two tailed test as the case is based on finding the difference of mileage with respect to countries.

c) A company has three categories of marketing analysts: (1) with professional qualifications but without work experience, (2) with professional qualifications and with work experience, and (3) without professional qualifications but with work experience. One of the study measures each analyst’s motivation level (classified as high, normal, and low). A hypothesis of no relation between analyst category and motivation is to be tested.

In this scenario where the categories with respect to the sample have been made and the responses has been classified as well, the most appropriate testing tool would be again chi square test as it is used to interpret data that is categorical in nature.

d) A company has 24 salespersons. The test must evaluate whether their sales performance is unchanged or has improved after a training program.

As mentioned in the case, the sales performance needs to evaluate based on the occurrence of event that is implementing a training program for them. According to the situation given in the case, the data used is dependent on various factors. In order to identify the performance of a company’s salespersons, 1 tailed t-test would be the most recommended solution as we need to measure the sales performance that is a quantitative measure.

Q2) You conduct a survey of a sample of 25 members of this year’s graduating business students and find that the average GPA is 3.2. The standard deviation of the sample is 0.4. Over the last 10 years, the average GPA has been 3.0.

I. Assume that the population is approximately normally distributed. Which statistic would you use to test whether this year’s average GPA is different than previous 10 years? Calculate the statistic.

II. Assume that we don’t know about the distribution of the population, but the sample size is 225. Which statistic would you use in this case? Calculate the statistic.

If there is no proper difference between the GPA of graduating students in this year and the average GPA of students for ten years, then the hypothesis is said to be a null hypothesis. In our case, we need to identify the variance that is change in the GPA of this year that is 3.2 with an average of ten years that is 3.0. T-test would be the appropriate one as the test is parametric in nature and the sample is one-sample thus, t-test would be the best and most valid option. The level of significance in this case is set to be around 0.05 and the value will be calculated...........................

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