Question

suppose that in a random selection of 100 colored candies, 30% of them are blue. the candy company claims that the percentage of blue candies is equal to 24%. use a 0.01 significance level to test that claim.

h₁: p>0.24

a. h₀: p = 0.24
h₁: p<0.24

b. h₀: p≠0.24
h₁: p = 0.24

c. h₀: p = 0.24
h₁: p≠0.24

identify the test statistic for this hypothesis test.
the test statistic for this hypothesis test is
(round to two decimal places as needed)

Explanation:

Step1: Calculate sample proportion

The sample proportion $\hat{p}$ is given as $0.30$ (since $30\% = 0.30$), the hypothesized proportion $p_0=0.24$, and the sample size $n = 100$.

Step2: Compute the test - statistic formula

The formula for the test - statistic $z$ in a one - sample proportion test is $z=\frac{\hat{p}-p_0}{\sqrt{\frac{p_0(1 - p_0)}{n}}}$.
Substitute the values: $\hat{p}=0.30$, $p_0 = 0.24$, and $n = 100$ into the formula.
First, calculate the denominator:

$$
LATEXBLOCK0
$$

Then, calculate the numerator: $\hat{p}-p_0=0.30 - 0.24=0.06$.
Now, find the $z$ - value: $z=\frac{0.06}{0.0427}\approx1.41$

Answer:

$1.41$