# Solved: Data analysis and decision making

## 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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