There is enough evidence to support the claim that the proportion of brand awareness of female TV viewers and the gender of the spokesperson are not independent (P-value = 0.01537).

Step-by-step explanation:

<em>The question is incomplete: the picture attached gives the missing sample data.</em>

This is a hypothesis test for the difference between proportions.

The claim that is going to be stated in the alternative hypothesis is that the proportion of brand awareness of female TV viewers and the gender of the spokesperson are not independent. This means that the proportions differ significantly.

Then, the null and alternative hypothesis can be written as:

$H_0: \pi_1-\pi_2=0\\\\H_a:\pi_1-\pi_2\neq 0$

The significance level is 0.05.

The sample 1 (Male celebrity), of size n1=150 has a proportion of p1=0.273.

$p_1=X_1/n_1=41/150=0.273$

The sample 2 (Female celebrity), of size n2=150 has a proportion of p2=0.407.

$p_2=X_2/n_2=61/150=0.407$

The difference between proportions is (p1-p2)=-0.133.

$p_d=p_1-p_2=0.273-0.407=-0.133$

The pooled proportion, needed to calculate the standard error, is:

$p=\dfrac{X_1+X_2}{n_1+n_2}=\dfrac{41+61.05}{150+150}=\dfrac{102}{300}=0.34$

The estimated standard error of the difference between means is computed using the formula:

$s_{p1-p2}=\sqrt{\dfrac{p(1-p)}{n_1}+\dfrac{p(1-p)}{n_2}}=\sqrt{\dfrac{0.34*0.66}{150}+\dfrac{0.34*0.66}{150}}\\\\\\s_{p1-p2}=\sqrt{0.001496+0.001496}=\sqrt{0.002992}=0.055$

Then, we can calculate the z-statistic as:

$z=\dfrac{p_d-(\pi_1-\pi_2)}{s_{p1-p2}}=\dfrac{-0.133-0}{0.055}=\dfrac{-0.133}{0.055}=-2.44$

This test is a two-tailed test, so the P-value for this test is calculated as (using a z-table):

$P-value=2\cdot P(z$

As the P-value (0.01537) is smaller than the significance level (0.05), the effect is significant.

The null hypothesis is rejected.

There is enough evidence to support the claim that the proportion of brand awareness of female TV viewers and the gender of the spokesperson are not independent (the proportions differ).

6 0

3 years ago

fruit o Rama sells dried pineapples 40.2 $5 per ounce mag spent a total of $2.65 on pineapples how many ounces did she buy

frozen [14]

She spend 10.6 ounces in a total of $2.65 on pineapples .

<u>Step-by-step explanation:</u>

Correct Question: fruit o Rama sells dried pineapples $0.25 per ounce mag spent a total of $2.65 on pineapples how many ounces did she buy .

We have , Rama sells dried pineapples $0.25 per ounce mag spent a total of $2.65 on pineapples . We need to find how many ounces did she buy . Le's find out:

According to Question , Rama sells dried pineapples $0.25 per ounce i.e. 1 pineapple cost 0.25 ounce . So, If he spends $2.65 in pineapples , Number of ounces he used is :

⇒ $\frac{2.65}{0.25}$

⇒ $\frac{265}{25}$

⇒ $\frac{25(10.6)}{25}$

⇒ $10.6$

Therefore , She spend 10.6 ounces in a total of $2.65 on pineapples .

3 0

4 years ago

Read 2 more answers