Answer:
Step-by-step explanation:
Subtract x from both sides.
Square both sides.
Subtract x²-6x+9 from both sides.
Factor left side of the equation.
Set factors equal to 0.
Check if the solutions are extraneous or not.
Plug x as 2.
x = 2 works in the equation.
Plug x as 6.
x = 6 does not work in the equation.
Answer:
Null hypothesis:
Alternative Hypothesis:
We have enough evidence to reject the null hypothesis at 10% level of significance.
Step-by-step explanation:
1) Data given
n =44, representing the sample size
represent the sample mean for the length of great white sharks
represent the sample standard deviation for the length of great white sharks
significance level for the test
2) Formulas to use
On this case we are intereste on the sample mean for the length of great white sharks, and based on the paragraph the hypothesis are given by:
Null hypothesis:
Alternative Hypothesis:
since we have n>30 but we don't know the population deviation so we will can use the t approximation. The sample mean have the following distribution
Based on this the statistic to check the hypothesis would be given by:
Replacing the values given we have:
We can calculate the degrees of freedom with:
With and the degrees of freedom we can calculate the critical value, since
we need a value from the t distribution with 43 degrees of freedom that accumulates 0.1 of the area on the right or 0.9 of the area on the left.
We can use excel, a calculator or a table for this, calculating this value we got:
Since our calculatesd value was , we can reject the null hypothesis at 0.1 level of significance.
Other way in order to have a criterion for reject or don't reject the null hypothesis is calculating the p value, on this case based on the alternative hypothesis the p value would be given by:
So then so we have enough evidence to reject the null hypothesis at 10% level of significance.