Answer to Question #337482 in Statistics and Probability for Pia

Question

DIRECTIONS: In each problem below, give the null and alternative hypothesis and

identify whether it is right-tailed, left-tailed or two-tailed test.

1. A newspaper report claims that 30% of all tea-drinkers prefer green tea to black tea.

Leo is 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.

2. A city had an employment rate of 70%. The mayor pledge to lower this figure and

supported programs to decrease unemployment. A group of citizens wanted to test if the

unemployment rate had actually decreased, so they obtained a random sample of citizens to see

what proportion of the sample was unemployed.

Answer 1

1. The null hypothesis states that 30% of all tea-drinkers prefer green tea will prefer green tea.

The alternative hypothesis states that not 30% of all tea-drinkers prefer green tea will prefer green tea.

$H_0: p=0.3$

$H_1: p\not=0.3$

B. This corresponds to a two-tailed test.

2. The null hypothesis states that an employment rate will be greater than or equal to 0.7.

The alternative hypothesis states that an employment ratewill be less than 0.7.

$H_0: p\ge0.7$

$H_1: p<0.7$

B. This corresponds to a left-tailed (directional, one-tailed) test.