1. Example
Malcheon Health Clinic claims that the average waiting time for a patient is 20 minutes with a population standard deviation of 7.26 minutes. A random sample of 15 patients yields a mean waiting time of minutes. At the 5% significance level, do the data indicate that the waiting time is longer than 20 minutes?
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2. Example
The sodium content of a popular sports drink is listed as 220mg in a 32-oz bottle. Analysis of 10 bottles indicates a sample mean of 228.2mg with a sample standard deviation of 18.2 mg. At the 10% significance level, do the data provide enough evidence to contradict the manufacturer’s claim?
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3. Hypothesis Test for a Single Population Proportion
For hypothesis tests regarding a population proportion, the test statistic is given by
where po is the value specified by the null hypothesis. Note that the test statistic will have a standard normal distribution if the null hypothesis is true.
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4. Example
Across the industry, cellular telephone providers expect that approximately 30% of their customers will switch providers (churn) at the end of their two-year contract. A provider decides to offer a random sample of 200 customers a free $350 “top of the line” phone if they renew their contract in order to determine whether this type of promotion would be effective in reducing churn. They find that only 20 of the customers refuse the offer and switch providers. Do the data provide sufficient evidence to conclude that this offer has effectively reduced churn? (e.g., the proportion of customers choosing to switch providers is less than 0.3)
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5. Example
A sample of 100 mortgages approved during the current year showed that 31 were issued to single-earner families or individuals. The historical percentage is 25%. At the 5% significance level, do the data indicate that the percentage of single-family or individual mortgages has increased?
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5/25/2019