Mathematics, 03.07.2020 02:01 sierravick123owr441

Ten years ago 53% of American families owned stocks or stock funds. Sample data collected by the Investment Company Institute indicate that the percentage is now 44%. (a) Choose the appropriate hypotheses such that rejection of H0 will support the conclusion that a smaller proportion of American families own stocks or stock funds this year than 10 years ago. H0: p - Select your answer - Ha: p - Select your answer - (b) Assume the Investment Company Institute sampled 300 American familie

Answers: 1

Show answers

Answers

Answer from: tevaughn06

a) The null and alternative hypothesis are:

$H_0: \pi=0.53\\\\H_a:\pi$

b) If 300 families were sampled, for a significance level of 5%, there is enough evidence to support the claim that a smaller proportion of American families own stocks or stock funds this year than 10 years ago (P-value = 0.001).

Step-by-step explanation:

The claim that we want to have evidence to support is that a smaller proportion of American families own stocks or stock funds this year than 10 years ago.

The hypothesis for this test should state:

- For the null hypothesis, that the population proportion is not significantly different from 53%.

$H_0:\pi=0.53$

- For the alternative hypothesis, that the population proportion is significantly less than 53%.

$H_a: \pi$

If 300 families are sampled, we can perform a hypothesis test for a proportion.

The claim is that a smaller proportion of American families own stocks or stock funds this year than 10 years ago.

Then, the null and alternative hypothesis are:

$H_0: \pi=0.53\\\\H_a:\pi$

The significance level is 0.05.

The sample has a size n=300.

The sample proportion is p=0.44.

The standard error of the proportion is:

$\sigma_p=\sqrt{\dfrac{\pi(1-\pi)}{n}}=\sqrt{\dfrac{0.53*0.47}{300}}\\\\\\ \sigma_p=\sqrt{0.00083}=0.029$

Then, we can calculate the z-statistic as:

$z=\dfrac{p-\pi+0.5/n}{\sigma_p}=\dfrac{0.44-0.53+0.5/300}{0.029}=\dfrac{-0.088}{0.029}=-3.065$

This test is a left-tailed test, so the P-value for this test is calculated as:

$\text{P-value}=P(z$

As the P-value (0.001) 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 a smaller proportion of American families own stocks or stock funds this year than 10 years ago.

Answer from: Quest

x= -3 and $x=\frac{-3+/-3i\sqrt{3} }{2}$

step-by-step explanation:

to find the roots of a cubic, use division or factoring to find the factors then set equal to 0. as this is a difference of cubes, it factors into

$(x^3-a^3)=$ $(x-a)(x^2+ax+a^2)$

where a is the cube root of $a^3$ .

here this is 27 and the cube root of 27 is 3. so we write using the form:

$(x-3)(x^2+(3)x+3^2)\\(x-3)(x^2+3x+9)$ .

set each factor to 0 and solve for x.

x-3=0

x=3

the quadratic expression does not factor and must be solved using the quadratic formula.

$x=\frac{-b+/-\sqrt{b^2-4ac} }{2a}$

where a = 1, b=3, and c=9

$x=\frac{-3+/-\sqrt{3^2-4(1)(9)} }{2(1)} \\x=\frac{-3+/-\sqrt{9-36)} }{2} \\x=\frac{-3+/-\sqrt{-27)} }{2}\\x=\frac{-3+/-3i\sqrt{3} }{2}$

this cubic has two complex roots.

Answer from: Quest

in problems involving proportions, we can use cross products to test whether two ratios are equal and form a proportion. to find the cross products of a proportion, we multiply the outer terms, called the extremes, and the middle terms, called the means.

hope it