Answer:
.
Step-by-step explanation:
The linear approximation is given by the equation
Linear approximation is a good way to approximate values of as long as you stay close to the point
, but the farther you get from
, the worse your approximation.
We know that,
Next, we need to plug in the known values and calculate the value of :
Then
.
Answer:
Step-by-step explanation:
The slope-intercept form of an equation of a line:
Convert the equation of a line 3x + 4x = 2y - 9 to the slope-intercept form:
<em>add 9 to both sides</em>
<em>divide both sides by 2</em>
Parallel lines have the same slope. Therefore we have the equation:
Put the coordinates of the point (4, -4) to the equation:
<em>subtract 14 from both sides</em>
Finally we have the equation:
Solution
Hypotheses:
- The population mean is 132. In order to test the claim that the mean is 132, we should check for if the mean is not 132.
- Thus, the Hypotheses are:
Test statistic:
- The test statistic has to be a t-statistic because the sample size (n) is less than 30.
- The formula for finding the t-statistic is:
- Applying the formula, we have:
Critical value:
- The critical value t-critical, is gotten by reading off the t-distribution table.
- For this, we need the degrees of freedom (df) which is gotten by the formula:
- And then we also use the significance level of 0.1 and the fact that it is a two-tailed test to trace out the t-critical. (Note: significance level of 0.1 implies 10% significance level)
- This is done below:
- The critical value is 1.729
P-value:
- To find the p-value, we simply check the table for where the t-statistic falls.
- The t-statistic given is 1.5747. We simply check which values this falls between in the t-distribution table. It falls between 1.328 and 1.729. We can simply choose a value between 0.1 and 0.05 and multiply the result by 2 since it is a two-tailed test.
- However, we can also use a t-distribution calculator, we have:
- Thus, the p-value is 0.13183
Final Conclusion:
- The p-value is 0.13183, and comparing this to the significance level of 0.1, we can see that 0.13183 is outside the rejection region.
- Thus, the result is not significant and we fail to reject the null hypothesis
