Alice rode her bicycle the same number of miles every day for 17 days. She

Find the 95% confidence interval for estimating the population mean μ

AVprozaik [17]

We first need to determine whether we are dealing with means or proportions in this problem. Since we are given the sample and population mean, we know that we are dealing with means.

Since we have one sample mean, this means we are creating a confidence interval for one sample (1 Samp T Int).

Normally we would check for conditions, but since this is not formulated as a "real-world scenario" type problem, it is hard to check for randomness and independence. Therefore, I will be excluding conditions from this answer.

<h3>Confidence Interval Formula</h3>

The formula for constructing a <u>confidence interval for means</u> is as follows:

$\displaystyle \overline{x} \pm t^*\big{(}\frac{\sigma}{\sqrt{n} } \big{)}$

We are given these variables:

$\overline{x}=50$
$n=60$
$\sigma=10$

Plug these values into the formula for the confidence interval:

$\displaystyle 50\pm t^* \big{(}\frac{10}{\sqrt{60} } \big{)}$

<h3>Finding the Critical Value (t*)</h3>

In order to find t*, we can use this formula:

$\displaystyle \frac{1-C}{2}=A$

Calculating the z-score associated with "A" will give us t*.

So, let's plug in the confidence interval 95% (.95) into the formula:

$\displaystyle \frac{1-.95}{2}=.025$

Use your calculator or a t-table to find the z-score associated with this area under the curve.. you should get:

$t^*=1.96$

<h3>Constructing Confidence Interval</h3>

Now, let's finish the confidence interval we created:

$\displaystyle 50\pm 1.96 \big{(}\frac{10}{\sqrt{60} } \big{)}$

We can calculate the confidence interval, using this formula, to be:

$\boxed{(47.4697, \ 52.5303)}$

<h3>Interpreting the Confidence Interval</h3>

We are 95% confident that the true population mean μ lies between <u>47.4697 and 52.5303</u>.

8 0

1 year ago

Two companies Company A and Company B offer the same starting salary of $20,000 per year. Company A gives a raise of $1000 each

Bingel [31]

A.) A = 20000 + 1000n
B = 20000(1.04)^n

b.) For A, sn = n/2(2a + (n - 1)d)
s20 = 20/2(2(20000) + 1000(20 - 1)) = 10(40000 + 19(1000)) = 10(40000 + 19000) = 10(59000) = $590,000
For B, sn = a(r^n - 1)/(r - 1)
s20 = 20000((1.04)^20 - 1)/(1.04 - 1) = 20000(2.191 - 1)/0.04 = 20000(1.191)/0.04 = 23822.46 / 0.04 = $595,561.57

c.) Using a graphing calculator, it takes 18 years for the
<span>total amount earned a company B is greater that the total amount of earned at company A.</span>

5 0

3 years ago

If matrix A is of the size 2×3 and we are able to add matrix B to A. what must be the size of B be?

tankabanditka [31]

Answer:

6 be because 2×3 =6 so B it will be the given answer

5 0

3 years ago

Please help me if you love your mom

kari74 [83]

Answer:

10.2 cm²

Step-by-step explanation:

regular hexagon made up of six equilateral triangles

A = (2 × 1.7) /2 × 6 = 10.2

or by the side length

A = 3√3/2 * 2² = 10.3

8 0

3 years ago

Turn 25/4 into a mixed number

horsena [70]

Mixed number is 6 1/4

3 0

3 years ago