There are two numbers whose difference is 1 and the sum of their squares is 61.

Ten years ago 53% of American families owned stocks or stock funds. Sample data collected by the Investment Company Institute in

stiks02 [169]

Answer:

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.

3 0

3 years ago

Sarah bought a lawnmower for $320. She signed up for the buy now pay later plan at the store with the following conditions: $100

marishachu [46]

Cost of the lawnmower bought by Sarah = $320
Amount of down payment made by Sarah = $100
Amount paid by Sarah in 12 months = (12 * 25) dollars
= 300 dollars
Total amount paid by Sarah = (300 + 100) dollars
= 400 dollars
Excess amount paid as interest by Sarah = (400 - 320) dollars
= 80 dollars
Actual yearly rate of interest paid by Sarah = (80/320) * 100 percent
= 25 percent
So 25% yearly interest was paid by Sarah. The correct option is option "C".

4 0

3 years ago

Solve the following proportion for X

mixer [17]

Answer: 3.7 (to nearest tenth)

Working:
7/17 = x/9
63 = 17x
x = 63/17
x = 3.7 (to nearest tenth)

8 0

3 years ago

Ryan planted 125 trees on my tree farm 28% of rum or maple trees and the rest of them are pine trees. Kioshi helped plant 125 tr

VashaNatasha [74]

Answer:

Ryan planted more maple trees than Kioshi.

Step-by-step explanation:

Given:

Total number of tress planted by Ryan = 125

Percent of maples tree planted by Ryan = 28%

Total number of tress planted by Kioshi = 125

We need to find who planted more maple trees.

Solution:

First we will find the number of maple tree planted by Ryan.

So we can say that;

the number of maple tree planted by Ryan is equal to Percent of maples tree planted by Ryan multiplied by Total number of tress planted by Ryan and then divided by 100.

framing in equation form we get;

the number of maple tree planted by Ryan = $\frac{28}{100}\times 125 = 35$