Katie invests $5,000 in an account earning 4% interest, compounded annually for 5 years. two years after katie's initial investment, emily invests $10,000 in an account earning 4% interest, compounded annually for 3 years. given that no additional deposits are made, compare the amount of interest earned after the interest period ends for each account. (round to the nearest dollar) a) katie earned $408 more in interest in her account than emily. b) emily earned $408 more in interest in her account than katie. c) katie earned $166 more in interest in her account than emily. d) emily earned $166 more in interest in her account than katie.

Emily earned $166 more in her account than Katie.

We use the compound interest formula for both of these:



For Katie's deposit:


This gives Katie 6083.26-5000 = 1083.26 in interest (1083, to the nearest dollar).

For Emily's deposit:


This means she earned 11248.64-10000=1248.64 in interest (1249, to the nearest dollar).

The difference in interest is given by 1249-1083=166

 

 

So the p value obtained was a very high value and using the significance level given we have 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 people said that blue is their favorite color is not differetn from 0.24 or 24% at 5% of significance.

Step-by-step explanation:

Data given and notation

n=75 represent the random sample taken

X=19 represent the number of people said that blue is their favorite color

estimated proportion of people said that blue is their favorite color

is the value that we want to test

represent the significance level

Confidence=95% or 0.95

z would represent the statistic (variable of interest)

represent the p value (variable of interest)  

Concepts and formulas to use  

We need to conduct a hypothesis in order to test the claim that the true proportion differs from 0.24 nor no.:  

Null hypothesis:  

Alternative hypothesis:  

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

(1)  

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

Calculate the statistic  

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

 

Statistical decision  

It's important to refresh the p value method or p value approach . "This method 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 provided . The next step would be calculate the p value for this test.  

Since is a bilateral test the p value would be:  

 

So the p value obtained was a very high value and using the significance level given we have 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 people said that blue is their favorite color is not differetn from 0.24 or 24% at 5% of significance.