Solved: Data analysis and decision making

Callaway is thinking about entering the golf ball market. The company will make a profit if its market share is more than 20%. A market survey indicates that 140 of 624 golf ball purchasers will buy a Callaway golf ball.

In your initial post, answer the following questions:

Is this enough evidence to persuade Callaway to enter the golf ball market?
How would you make the decision if you were Callaway management? Would you use hypothesis testing?

Expert Partial Solution 

Step I: stating the null (Ho) and alternative (Ha) hypotheses: According to Albright & Winston (2017 p.364), an alternative hypothesis is the hypothesis an analyst tries to prove. Null hypothesis, on the other hand, refers to the current thinking or the accepted theory that an analyst attempts to disprove (p.365). In this problem, we want to figure out whether the sample proportion exceeds 20% and hence, the hypotheses can be set up as follows:

H_o: p = 0.2

H_a: p > 0.2

Where p represents proportion of customers purchasing golfs at Callaway

Callaway would like to prove that it will make a profit if its market share is more than 20% (H_a). The opposite, that Callaway will make a profit if its market share equals 20%, becomes the null hypothesis. One of these possibilities must be true, and our goal is to use the provided sample data to determine which is true.

Step II: choosing the significance level (α): The select significance level of test is 0.05. This is the value of α that I will use to determine the rejection region (the set of sample data that leads to the rejection of the null hypothesis p.368).

Step III:  calculating the test statistic (p-value): According to the text, “The p-value of a sample is the probability of seeing a sample with at least as much evidence in favor of the alternative hypothesis as the sample actually observed” (p. 369). If the calculated p-value is less than 0.05, I will reject the H_o and conclude that H_a is statistically significant. If the calculated p-value is greater than 0.05, I will fail to reject the H_o and determine the difference is not statistically significant… Read more

Step IV: comparing the p-value to alpha: I will reject the null hypothesis (H_o) if the calculated P-value is less than 0.05- the significance level.

Step V: Making a decision: Hypothesis testing has been done using z-test for the mean, t-test for the mean, and z-test for the proportion. In every test, I have varied the alpha (α) to avoid committing type I error (by incorrectly rejecting the null hypothesis yet it is true) and type II error (by incorrectly accepting the null hypothesis yet it is false) (p.367). In the z-test for the mean, there is 0.025% of the sample in each tail when using the select alpha (0.05). From the computations, the alpha has critical values of -1.96 and 1.96 and because the z-value (1.73) falls within this range, I fail to reject the null hypothesis...Read More

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Solved: Data analysis and decision making