Mathematics, 26.03.2020 21:12 wiredq2049

A car company says that the mean gas mileage for its luxury sedan is at least 24 miles per gallon (mpg). You believe the claim is incorrect and find that a random sample of 5 cars has a mean gas mileage of 23 mpg and a standard deviation of 5 mpg. At alpha equals 0.10, test the company's claim. Assume the population is normally distributed.

Answers: 2

Show answers

Answers

Answer from: genyjoannerubiera

$t=\frac{23-24}{\frac{5}{\sqrt{5}}}=-0.447$

$p_v =P(t_{(4)}$

If we compare the p value and the significance level given $\alpha=0.1$ we see that $p_v\alpha$ so we can conclude that we have enough evidence to fail reject the null hypothesis, so we can't reject the claim that the true mean is at least 24 mpg (null hypothesis) at 1% of signficance.

Step-by-step explanation:

Data given and notation

$\bar X=23$ represent the sample mean

s=5 represent the sample standard deviation for the sample

n=5 sample size

$\mu_o =24$ represent the value that we want to test

$\alpha=0.1$ 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 mean is lower than 24 (rejecting the claim proposed), the system of hypothesis would be:

Null hypothesis: $\mu \geq 24$

Alternative hypothesis: $\mu < 24$

If we analyze the size for the sample is < 30 and we don't know the population deviation so 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:

$t=\frac{23-24}{\frac{5}{\sqrt{5}}}=-0.447$

P-value

The first step is calculate the degrees of freedom, on this case:

df=n-1=5-1=4

Since is a one sided test the p value would be:

$p_v =P(t_{(4)}$

Conclusion

Answer from: Quest

for this case we have the following expression:

$\frac {8} {\frac {1} {6}}$

to solve, we rewrite the expression as:

$\frac {\frac {8} {1}} {\frac {1} {6}} =$

we apply double c and we have:

$\frac {6 * 8} {1} =\\48$

thus, the quotient is 48.

so, patel found a wrong ratio and the multiplication was incorrect.

option d

Answer from: Quest

D. i think it is the savings

Another question on Mathematics

Mathematics, 21.06.2019 12:30

And explain how you got it so i can understand future problems : 3

Answers: 1

Answer

Mathematics, 21.06.2019 19:00

You are at a restaurant and owe $38 for your meal. you want to leave a 20% tip. how much will your tip be?

Answers: 1

Answer

Mathematics, 21.06.2019 19:30

Ariel is working at a meat packing plant for 5 nights a week. her regular wage is $11 an hour. she earns tine and a half for any overtime hours. this week she worked 9 hours of over time .how much will ariel earn for overtime this week ?

Answers: 1

Answer

Mathematics, 21.06.2019 21:30

Jalen charges $25.50 for every 3 hours of yard work he does for his neighbors. ralph charges $34 for every 4 hours of work that he does. who charges less? opinions: 1.they charge the same amount 2.jalen 3.ralph

Answers: 1

Answer

You know the right answer?

A car company says that the mean gas mileage for its luxury sedan is at least 24 miles per gallon (m...

Questions