We have been given an image of a trapezoid. We are asked to find the measure of angle M and N.
We know that bases of trapezoid are parallel and the two angles between two parallel lines are supplementary, so we can set an equation as:
Upon substituting value of y in measure of angle M, we will get:
Therefore, measure of angle M is 110 degrees.
Similarly, we will find the value of angle N as:
Therefore, measure of angle N is 70 degrees.
Answer:
a) The null and alternative hypothesis are:
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%.
- For the alternative hypothesis, that the population proportion is significantly less than 53%.
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:
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:
Then, we can calculate the z-statistic as:
This test is a left-tailed test, so the P-value for this test is calculated as:
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.