A nationwide survey of entrepreneurs in Vietnam was conducted to gather informat

Question

A nationwide survey of entrepreneurs in Vietnam was conducted to gather information about the perceptions and intentions of entrepreneurs in this emerging economy. Participants were asked (among other things) their age and to estimate the chance of success of their current entrepreneurial endeavor. A researcher is interested in determining if the age of the respondent affects their estimate of their chance of success. Use the information in the table below to conduct an appropriate hypothesis test to determine if "Age" is independent from "Chance of Success". Be sure to state your hypotheses, test statistic, degrees of freedom (if applicable), and p-value. Use alpha = 0.05.

Explanation / Answer

We will be using Chi-Square Test for Independence for the hypothesis test.

State the hypotheses. The first step is to state the null hypothesis and an alternative hypothesis.

H0: Age and Chance of Success are independent.
Ha: Age and Chance of Success are not independent.

Formulate an analysis plan. For this analysis, the significance level is 0.05. Using sample data, we will conduct a chi-square test for independence.

Analyze sample data. Applying the chi-square test for independence to sample data, we compute the degrees of freedom, the expected frequency counts, and the chi-square test statistic. Based on the chi-square statistic and the  degrees of freedom, we determine the P-value.

Let r be number of rows and c is number of columns

DF = (r - 1) * (c - 1) = (4-1) * (2-1) = 3

We will be calculating the expected counts by the formula. Er,c = (nr * nc) / n

It is given in the below table.

Chi Square test statistic is

2 = [ (Or,c - Er,c)2 / Er,c ]
2 = (34 - 35.48)2/35.48 + (32 - 30.52)2/30.52 + (52 - 45.16)2/45.16 + (32 - 38.84)2/38.84 + (124 - 134.41)2/134.41 + (126 - 115.59)2/115.59 + (40 - 34.95)2/34.95 + (25 - 30.05)2/30.05

= 5.6962

So, Test statistic is 5.6962

For df = 3, we use the Chi-Square Distribution Calculator to find P(2 > 5.6962) = 0.1274

So, p-value = 0.1274

Interpret results and Conclusion. Since the P-value (0.1274) is greater than the significance level (0.05), we fail to reject the null hypothesis. Thus, we conclude that there is no relationship between Age and Chance of Success and Age and Chance of Success are independent.

Chance of Success Age 21 or Younger Age Over 21 Total Certain 34 32 66 High 52 32 84 Medium 124 126 250 Low 40 25 65 Total 250 215 465

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