## Related questions with answers

A software company is trying to decide whether to produce an upgrade of one of its programs. Customers would have to pay $100 for the upgrade. For the upgrade to be profitable, the company has to sell it to more than 20% of their customers. You contact a random sample of 60 customers and find that 16 would be willing to pay$100 for the upgrade. Do the sample data give convincing evidence at the $\alpha=0.05$ significance level that more than 20% of the company's customers are willing to purchase the upgrade?

Solution

VerifiedGiven:

$\begin{align*} \alpha&=\text{Significance level}=0.05 \\ n&=\text{Sample size}=60 \\ x&=\text{Number of successes}=16 \end{align*}$

Given claim: more than 20%

The claim is either the null hypothesis or the alternative hypothesis. The null hypothesis states that the population proportion is equal to the value mentioned in the claim. If the null hypothesis is the claim, then the alternative hypothesis states the opposite of the null hypothesis.

$\begin{align*} H_0&:p=20\%=0.20 \\ H_a&:p>0.20 \end{align*}$

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