Two intersecting lines have zero, an infinite number, two, or one of the same points in common?

Mathematics

1 answer:

KIM [24]3 years ago

6 0

If two lines intersect, then there are two possibilities

A) The lines intersect at exactly one point. This happens if the slopes of the two lines are different (the y intercepts may or may not be the same).

B) The lines intersect at infinitely many points. This happens when both slopes are the same and when both y intercepts are the same. In short, the two equations are identical. Often they may be written in different forms. For example, the equation y = 2x+1 and 2y = 4x+2 are the same equation. Divide everything in equation (2) by 2 and you'll get equation (1).

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A well-known brokerage firm executive claimed that at least 41 % of investors are currently confident of meeting their investmen

atroni [7]

Answer:

$z=\frac{0.398 -0.41}{\sqrt{\frac{0.41(1-0.41)}{88}}}=-0.229$

Step-by-step explanation:

1) Data given and notation n

n=88 represent the random sample taken

X=35 represent the adults that said they are confident of meeting their goals

$\hat p=\frac{35}{88}=0.398$ estimated proportion of adults that said they are confident of meeting their goals

$p_o=0.41$ is the value that we want to test

$\alpha$ represent the significance level

z would represent the statistic (variable of interest)

$p_v$ represent the p value (variable of interest)

2) Concepts and formulas to use

We need to conduct a hypothesis in order to test the claim that that at least 41 % of investors are currently confident of meeting their investment goals.:

Null hypothesis: $p=0.41$

Alternative hypothesis: $p < 0.41$

When we conduct a proportion test we need to use the z statisitc, and the is given by:

$z=\frac{\hat p -p_o}{\sqrt{\frac{p_o (1-p_o)}{n}}}$ (1)

The One-Sample Proportion Test is used to assess whether a population proportion $\hat p$ is significantly different from a hypothesized value $p_o$ .

3) Calculate the statistic

Since we have all the info requires we can replace in formula (1) like this:

$z=\frac{0.398 -0.41}{\sqrt{\frac{0.41(1-0.41)}{88}}}=-0.229$

4) Statistical decision

It's important to refresh the p value method or p value approach . "This methos is about determining "likely" or "unlikely" by determining the probability assuming the null hypothesis were true of observing a more extreme test statistic in the direction of the alternative hypothesis than the one observed". Or in other words is just a method to have an statistical decision to fail to reject or reject the null hypothesis.

The significance level is not provided, but we can assume $\alpha=0.05$ . The next step would be calculate the p value for this test.

Since is a unilateral test the p value would be:

$p_v =P(z$

Using the p value obtained and the significance level assumed $\alpha=0.05$ we have $p_v>\alpha$ so we can conclude that we have enough evidence to FAIL to reject the null hypothesis, and we can said that at 5% of significance the proportion of of investors that are currently confident of meeting their investment goals is not significantly lower than 0.41 or 41%.