Question

1. Describe the type of analysis that would be performed in each situation, selecting from the options below. Using complete sentences, explain your reasoning.

Types of analysis:     Confidence interval for a population proportion

Confidence interval for a population mean (z-interval)

Confidence interval for a population mean (t-interval)

One-sample z-test for population proportion

One-sample z-test for population mean

One-sample t-test for population mean

1. A company claims that “Nine out of 10 customers would recommend us to a friend”. A researcher thinks this number sounds high, so she surveys a random sample of customers from the previous 18 months.

2. A gardener has recently moved to Oregon and wants to know what the average weekly rainfall is before deciding whether or not to install an irrigation system. He measures the amount of rainfall each week using a rain gauge.

3. There is some debate regarding whether 98.6 °F should be considered the normal body temperature for a healthy adult. A recent research study found the mean body temperature of a sample of healthy adults to be 98.2 °F.

Answer 1

i)

One-sample z-test for the population proportion. because recommending a friend is a qualitative variable. So, we calculate the proportion in this case.

ii)

Confidence interval for a population mean (z-interval). when n is large

Confidence interval for a population mean (t-interval) when n is small

Because he wants to know the average rainfall and he is not claiming any mean value. That's why the confidence interval.

iii)

One-sample z-test for population mean. when n is large

One-sample t-test for population mean. when n is small

he wants to test for mean and he is claiming a value 98.6 for which he will test the hypothesis.