The last line of a proof represents

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

When a problem involves more than one unit for a characteristic (such as length), now can you tell which unit is more appropriat

Lostsunrise [7]

Answer:

For larger measurements, we use larger unit while for smaller measurement we use smaller unit.

Step-by-step explanation:

Normally, For larger distances we make use of larger units while for smaller distances we make use of smaller units.

For example, if we consider the distance travelled by a person in some days;

For 15000 units distance; We can represent this value as 15 Kilometers

For 800 units distance; Rather than using kilometers, it would be better to represent it in meters as 8 meters.

Also, For 70 units distance; Instead of kilometers or meters, 70 cm would be a better unit of representation.

Likewise, If we consider some 3 dimensional shapes holding some substances,

For 7000 units, best unit of weight representation would be 7 Kg

For 600 units, instead of in kg, best unit of weight representation would be 600 grams

For 50 units, best unit of weight representation would be 50 grams

So, looking at the examples given in both weight and distances, we will conclude that for larger measurements, we use larger unit while for smaller measurement we use smaller unit.

7 0

3 years ago

Solving Exponential and Logarithmic Equation In exercise,solve for x or t.See example 5 and 6.

nalin [4]

Answer:x=15

Step-by-step explanation:

You should collect the like terms first

21-6=x

Therefore

X=15

6 0

3 years ago