Question

Write the statistical hypotheses for each of the following after determining if they are one-tailed or two-tailed. A research company concludes that 42% of adults seek advice from a primary care practitioner before seeing a specialist. A researcher wants to test this conclusion. A physician makes 5.8 recommendations per day to patients with respect to taking OTC supplements. A researcher believes this is less than the true number of recommendations. The mean age of nurses has been reported to be 46.2 in a recent study. This seems too young, and another researcher wants to test to determine if the average is greater than this. According to the U.S. Department of Labor, in 2010 the average out-of-pocket expense for a family of four on health expenditures is $3,589 annually. An insurance company commissions a study to determine if this number is still the average out-of-pocket expense.

Answer 1

Part 1

A research company concludes that 42% of adults seek advice from a primary care practitioner before seeing a specialist. A researcher wants to test this conclusion.

Null hypothesis: H₀: The percentage of adults who seek advice from a primary care practitioner before seeing a specialist is 42%.

Alternative hypothesis: H_a: The percentage of adults who seek advice from a primary care practitioner before seeing a specialist is not 42%.

H₀: p = 0.42 versus H_a: p ≠ 0.42

This is a two tailed test.

Part 2

A physician makes 5.8 recommendations per day to patients with respect to taking OTC supplements. A researcher believes this is less than the true number of recommendations.

Null hypothesis: H₀: A physician makes 5.8 recommendations per day to patients with respect to taking OTC supplements.

Alternative hypothesis: H_a: A physician makes less than 5.8 recommendations per day to patients with respect to taking OTC supplements.

H₀: µ = 5.8 versus H_a: µ < 5.8

This is a lower tailed or left tailed test. This is a one tailed test.

Part 3

The mean age of nurses has been reported to be 46.2 in a recent study. This seems too young, and another researcher wants to test to determine if the average is greater than this.

Null hypothesis: H₀: The mean age of nurses is 46.2 years.

Alternative hypothesis: H_a: The mean age of nurses is greater than 46.2 years.

H₀: µ = 46.2 versus H_a: µ > 46.2

This is an upper tailed or right tailed test. This is a one tailed test.

Part 4

According to the U.S. Department of Labor, in 2010 the average out-of-pocket expense for a family of four on health expenditures is $3,589 annually. An insurance company commissions a study to determine if this number is still the average out-of-pocket expense.

Null hypothesis: H₀: The average out-of-pocket expense for a family of four on health expenditures is $3,589 annually.

Alternative hypothesis: H_a: The average out-of-pocket expense for a family of four on health expenditures is not $3,589 annually.

H₀: µ = $3,589 versus H_a: µ ≠ $3,589

This is a two tailed test.