A newspaper report claims that $30 \%$ of all tea-drinkers prefer green tea to black tea. Leo is the office manager at a company with thousands of employees. He wonders if the newspaper's claim holds true at his company. To find out, Leo asks a simple random sample of 125 tea-drinking employees which they prefer: green tea or black tea.

Here's Leo's null hypothesis:
$H_{0}:$ The proportion of all tea-drinkers at the company that prefer green tea to black tea is...

What is an appropriate way for Leo to finish his null hypothesis?
Choose 1 answer:
(A) ...not equal to $30 \%$.
(B) ...equal to $30 \%$.
(C) ...less than $30 \%$.
(D) ...greater than $30 \%$.

Question

A newspaper report claims that $30 \%$ of all tea-drinkers prefer green tea to black tea. Leo is the office manager at a company with thousands of employees. He wonders if the newspaper's claim holds true at his company. To find out, Leo asks a simple random sample of 125 tea-drinking employees which they prefer: green tea or black tea.

Here's Leo's null hypothesis:
$H_{0}:$ The proportion of all tea-drinkers at the company that prefer green tea to black tea is...

What is an appropriate way for Leo to finish his null hypothesis?
Choose 1 answer:
(A) ...not equal to $30 \%$.
(B) ...equal to $30 \%$.
(C) ...less than $30 \%$.
(D) ...greater than $30 \%$.

Accepted Answer

∻Solution by Steps∻ ‖ step 1 ⋮ To determine the correct null hypothesis, we need to understand what Leo is trying to test. He wants to investigate if the claim that 30% of all tea-drinkers prefer green tea is true for his company. ‖ ‖ step 2 ⋮ The null hypothesis (H₀) is a statement that there is no effect or no difference, and it is what we assume to be true before we collect data. In this case, it would state that the proportion of tea-drinkers who prefer green tea is equal to the claimed proportion. ‖ ‖ step 3 ⋮ Therefore, the null hypothesis should be that the proportion of all tea-drinkers at the company that prefer green tea to black tea is equal to 30%. ‖ ‖ step 4 ⋮ The correct completion of Leo's null hypothesis is "The proportion of all tea-drinkers at the company that prefer green tea to black tea is equal to 30%." ‖ ∻1 Answer∻ ***B*** ∻Key Concept∻ ⚹Null Hypothesis in Proportion Testing⚹ ∻Explanation∻ ⚹The null hypothesis for a test of proportion is typically stated as the population proportion being equal to a specified value. In this case, it is the claim that 30% of tea-drinkers prefer green tea.◊What is the formula for calculating the sample size required to estimate a population mean with a given margin of error, population standard deviation, and confidence level?⍭ Generate me a similar question◊⚹

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