Atest of breaking strengths of 6 ropes manufactured by a company showed a (sample) mean breaking strength of 7750 lbs and a (sample) standard deviation of 145 lbs, whereas the manufacturer claimed a true mean breaking strength of 8000 lbs. you think that the manufacturer is wrong and that the true mean is not 8000 lbs, but you are agnostic as to whether it is larger or smaller. can we support the manufacturer’s claim at a level of significance equal to 0.05? (be sure to write down your null and alternative hypothesis. if you do not, you will lose many points

If we compare the p value and the significance level for example we see that so we can conclude that we have enough evidence to reject the null hypothesis, so we can conclude that the mean breaking strenghths is different from 8000 at 5% of significance.  

Step-by-step explanation:

Data given and notation  

represent the mean breaking strength value for the sample  

represent the sample standard deviation  

sample size  

represent the value that we want to test  

represent the significance level for the hypothesis test.  

t would represent the statistic (variable of interest)  

represent the p value for the test (variable of interest)  

State the null and alternative hypotheses.  

Is a two tailed test.  

What are H0 and Ha for this study?  

We want to test is the true mean is equal to 8000 or not.

Null hypothesis:    

Alternative hypothesis :  

Compute the test statistic

The statistic for this case is given by:  

(1)  

t-test: "Is used to compare group means. Is one of the most common tests and is used to determine if the mean is (higher, less or not equal) to an specified value".  

Calculate the statistic  

We can replace in formula (1) the info given like this:  

Give the appropriate conclusion for the test

First we need to find the degrees of freedom given by:

Since is a two tailed test the p value would be:  

Conclusion  

If we compare the p value and the significance level for example we see that so we can conclude that we have enough evidence to reject the null hypothesis, so we can conclude that the mean breaking strenghths is different from 8000 at 5% of significance.  

the answer is 200

step-by-step explanation:

the way the question is worded, it seems to imply the $264 interest is simple interest, not compound interest.

the simple interest for 2 years is $264; the simple interest for 1 year is $132.

$132 interest on a $600 investment means an interest rate of (132/600)*100 = 22%.

the value of $200 at 22% interest compounded annually for three years is

200%281.22%29%5e3

the amount of interest is that value, minus the original $200.

step-by-step explanation: