Question

A toothpaste company wants to declare in an ad that more than 80% of dentists recommend their toothpaste. The company performs a hypothesis test at the α = 0.05 significance level to test their claim.

The company samples 300 dentists. Of these, 243 recommend their toothpaste.

Let p represent the population proportion of dentists that recommend their toothpaste.

a. Specify the null and alternative hypotheses for the company's claim.

multiple choice 1

H₀: p = 0.80; HA: p > 0.80

H₀: p = 0.80; HA: p < 0.80

H₀: p = 0.80; HA: p ≠ 0.80

Answer 1

The null hypothesis is H₀: p = 0.80 and the alternative hypothesis is Hᴇ: p > 0.80, reflecting the company's claim of more than 80% dentist recommendations. So the correct answer is option A.

Step-by-step explanation:

The null and alternative hypotheses for the toothpaste company's claim where they want to declare that more than 80% of dentists recommend their toothpaste are as follows:

• H₀: p = 0.80
• Hᴇ: p > 0.80

Here, H₀ (null hypothesis) specifies the existing state of belief (80% of dentists recommend the toothpaste), and Hᴇ (alternative hypothesis) represents the company's claim that more than 80% of dentists recommend their product. Since the company wants to prove 'more than' a specific value, the alternative hypothesis is expressed with a '>' sign.