Find an equation for the line that passes through the points , −6−2 and , 4−6 .

An automobile manufacturer who wishes to advertise that one of its models achieves 30 mpg (miles per gallon) decides to carry ou

Katyanochek1 [597]

Answer:

$t=\frac{29.35-30}{\frac{1.365}{\sqrt{6}}}=-1.17$

$p_v =P(t_{(5)}$

If we compare the p value and the significance level given $\alpha=0.05$ we see that $p_v>\alpha$ so we can conclude that we have enough evidence to FAIL to reject the null hypothesis.

We can say that at 5% of significance the true mean is not significantly less than 30 so then the claim that true average fuel efficiency is (at least) 30 mpg makes sense

Step-by-step explanation:

Data given and notation

The mean and sample deviation can be calculated from the following formulas:

$\bar X =\frac{\sum_{i=1}^n x_i}{n}$

$s=\sqrt{\frac{\sum_{i=1}^n (x_i -\bar X)}{n-1}}$

$\bar X=29.35$ represent the sample mean

$s=1.365$ represent the sample standard deviation

$n=6$ sample size

$\mu_o =30$ represent the value that we want to test

$\alpha=0.05$ represent the significance level for the hypothesis test.

t would represent the statistic (variable of interest)

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

State the null and alternative hypotheses.

We need to conduct a hypothesis in order to check if the true mean is lower than 30 or no, the system of hypothesis are :

Null hypothesis: $\mu \geq 30$

Alternative hypothesis: $\mu < 30$

Since we don't know the population deviation, is better apply a t test to compare the actual mean to the reference value, and the statistic is given by:

$t=\frac{\bar X-\mu_o}{\frac{s}{\sqrt{n}}}$ (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:

$t=\frac{29.35-30}{\frac{1.365}{\sqrt{6}}}=-1.17$

P-value

We need to calculate the degrees of freedom first given by:

$df=n-1=6-1=5$

Since is a one-side left tailed test the p value would given by:

$p_v =P(t_{(5)}$

Conclusion

If we compare the p value and the significance level given $\alpha=0.05$ we see that $p_v>\alpha$ so we can conclude that we have enough evidence to FAIL to reject the null hypothesis.

We can say that at 5% of significance the true mean is not significantly less than 30 so then the claim that true average fuel efficiency is (at least) 30 mpg makes sense

5 0

3 years ago

What is 3X +7 equals five

NNADVOKAT [17]

$3x + 7 = 5$

$3x = 5 - 7$

$3x = - 2$

$x = \frac{ - 2}{3}$

5 0

3 years ago

Please help! Greatly appreciated

Pavlova-9 [17]

$\boxed{\sf 11, 7}\boxed$

Isolate this variable, x, by dividing each side by factors that do not contain the variable.

6 0

2 years ago

How do I solve this

kap26 [50]

For 3 find the total area for the big semicircle, then find the area of the smaller one and subtract it. It would be the same for 4 but instead you find the total area of the square (24 x 24) and then subtract the semicircle are. (you were wrong on #4)

6 0

3 years ago

the black triange in the first quadrant is the original figure label each other triangle with its transformation PLS HELP ASAP 6

Olenka [21]

Answer:

Step-by-step explanation:

Transformation from figure 1 to figure 2,

Translation of figure 1 by 6 units to the left.

Transformation of figure 1 to figure 3,

Reflection of figure 1 across y-axis.

Transformation from figure 1 to figure 4,

Translation of figure 1 by 6 units to the left and 4 units down.

Transformation from figure 1 to figure 5,

Translation of figure 1 by 3 units left and 6 units down.

Transformation from figure 1 to figure 6,

Reflection of figure 1 across x-axis.

4 0

3 years ago