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Suppose μ1 and μ2 are true mean stopping distances at 50 mph for cars of a certain type equipped with two different types of bra

Stella [2.4K]

Answer:

The 95% confidence interval would be given by $-23.44 \leq \mu_1 -\mu_2 \leq -8.16$

Step-by-step explanation:

Previous concepts

A confidence interval is "a range of values that’s likely to include a population value with a certain degree of confidence. It is often expressed a % whereby a population means lies between an upper and lower interval".

The margin of error is the range of values below and above the sample statistic in a confidence interval.

Normal distribution, is a "probability distribution that is symmetric about the mean, showing that data near the mean are more frequent in occurrence than data far from the mean".

$\bar X_1 =114.1$ represent the sample mean 1

$\bar X_2 =129.9$ represent the sample mean 2

n1=5 represent the sample 1 size

n2=2 represent the sample 2 size

$s_1 =5.08$ sample standard deviation for sample 1

$s_2 =5.37$ sample standard deviation for sample 2

$\mu_1 -\mu_2$ parameter of interest.

Confidence interval

The confidence interval for the difference of means is given by the following formula:

$(\bar X_1 -\bar X_2) \pm t_{\alpha/2}\sqrt{\frac{s^2_1}{n_1}+\frac{s^2_2}{n_2}}$ (1)

The point of estimate for $\mu_1 -\mu_2$ is just given by:

$\bar X_1 -\bar X_2 =114.1-129.9=-15.8$

In order to calculate the critical value $t_{\alpha/2}$ we need to find first the degrees of freedom, given by:

$df=n_1 +n_2 -1=5+5-2=8$

Since the Confidence is 0.95 or 95%, the value of $\alpha=0.05$ and $\alpha/2 =0.025$ , and we can use excel, a calculator or a table to find the critical value. The excel command would be: "=-T.INV(0.025,8)".And we see that $t_{\alpha/2}=\pm 2.31$

The standard error is given by the following formula:

$SE=\sqrt{\frac{s^2_1}{n_1}+\frac{s^2_2}{n_2}}$

And replacing we have:

$SE=\sqrt{\frac{5.08^2}{5}+\frac{5.37^2}{5}}=3.306$

Confidence interval

Now we have everything in order to replace into formula (1):

$-15.8-2.31\sqrt{\frac{5.08^2}{5}+\frac{5.37^2}{5}}=-23.437$

$-15.8+2.31\sqrt{\frac{5.08^2}{5}+\frac{5.37^2}{5}}=-8.163$

So on this case the 95% confidence interval would be given by $-23.44 \leq \mu_1 -\mu_2 \leq -8.16$

8 0

3 years ago

Suppose a rollerblade racer finished a 132 meter race in 18 seconds. What is the average speed of the rollerblade racer?

fomenos

C
the answer on a calculator is 7.33333...

8 0

3 years ago

Read 2 more answers

Please! Help! The table below shows preferences of dancing or playing sports for male and female students:

Kryger [21]

Answer:

D) He calculated the joint relative frequency of female students who prefer playing sports. The conditional relative frequency for female students who prefer playing sports is 34%.

Step-by-step explanation:

The table is given as:

Playing sports Dancing Row totals

Male students 18 16 34

Female students 18 35 53

Column totals 36 51 87

We know that the joint relative frequency of an outcome is calculated as dividing the frequency of the outcome by the grand total.

Hence, when we divide the frequency of the female students who prefer playing sports i.e. 18 by the grand total i.e. 87 ; we obtain:

18/87=0.20689

which is approximately equal to 21%.

Hence, in order to calculate the conditional relative frequencies she should have divided the required frequency by the row total;.

Hence, here we divide the frequency of the female students who prefer playing sports i.e. 18 by the row total i.e. 53 ; we obtain:

18/53-0.3396

which is approximately equal to 34%.

Hence, option: D is correct.

5 0

3 years ago

Read 2 more answers

What would you do to solve the system?

Molodets [167]

Answer:

To decide whether to add or subtract, determine if the values of the coefficients are the same or opposites:

. If the values are the same, subtract the equations.

• If the values are opposites or additive inverses, add the equations.

Step-by-step explanation:

Given

$12x = 48 - 8y$

$10x + 8y = 38$

Required

How to solve

Options (1) and (2) are incorrect because none of the options eliminate x or y.

For option (3),

- Check for the coefficients of x and y

- If they are the same (sign and value), then subtract; otherwise add

For instance:

$12x = 48 - 8y$

$10x + 8y = 38$

Rewrite the second equation

$12x = 48 - 8y$

$10x = 38 - 8y$

The coefficient of y are the same, so we subtract;

$12x - 10x = 48 - 38 -8y -(-8y)$

$12x - 10x = 48 - 38 -8y +8y$

$2x = 10$

$x= 5$

<em>See that y has been eliminated</em>

8 0

3 years ago

Annie has 385 flowers she has 238 less than Zoe how many flowers does Zoe have

lord [1]

Answer:

623

Step-by-step explanation:

Add 385 to 238

7 0

3 years ago