2/4 and 20/36 a proportional yes/no

UCF believes that the average time someone spends in the gym is 56 minutes. The university statistician takes a random sample of

11111nata11111 [884]

Answer:

We conclude that the average time someone spends in the gym is different from 56 minutes.

Step-by-step explanation:

We are given that UCF believes that the average time someone spends in the gym is 56 minutes.

The university statistician takes a random sample of 32 gym goers and finds the average time of the sample was 50 minutes. Assume it is known the standard deviation of time all people spend in the gym is 8 minutes.

Let $\mu$ = population average time someone spends in the gym

SO, Null Hypothesis, $H_0$ : $\mu$ = 56 minutes {means that the average time someone spends in the gym is 56 minutes}

Alternate Hypothesis, $H_A$ : $\mu\neq$ 56 minutes {means that the average time someone spends in the gym is different from 56 minutes}

The test statistics that will be used here is One-sample z test statistics as we know about the population standard deviation;

T.S. = $\frac{\bar X -\mu}{\frac{\sigma}{\sqrt{n} } }$ ~ N(0,1)

where, $\bar X$ = sample average time someone takes in the gym = 50 min

$\sigma$ = population standard deviation = 8 minutes

n = sample of gym goers = 32

So, test statistics = $\frac{50-56}{\frac{8}{\sqrt{32} } }$

= -4.243

Since in the question we are not given the level of significance so we assume it to b 5%. Now at 5% significance level, the z table gives critical value between -1.96 and 1.96 for two-tailed test. Since our test statistics does not lie within the range of critical values of z so we have sufficient evidence to reject our null hypothesis as it will fall in the rejection region.

Therefore, we conclude that the average time someone spends in the gym is different from 56 minutes.

4 0

3 years ago

Questions are in the screenshot.

White raven [17]

For question 4, $x = 18$ units,

For question 5, $x = 8.333$ units.

Step-by-step explanation:

Step 1:

Since the given polygons are similar to each other, all the ratios of one polygon to the other will remain equal for all the values of the two similar polygons.

We take the ratio of the same sides of both polygons i.e. the ratio of the lengths or the ratio of the widths.

Step 2:

For question 4, the first rectangle has a length of 9 units while the width is 3 units.

For the second rectangle, the length is x as x is greater than the width in the first rectangle. The width is 6 units.

The ratio of the first rectangle to the second is;

$\frac{3}{6} : \frac{9}{x} , x = (9)(\frac{6}{3} ) = 18.$ So $x = 18$ units.

Step 3:

The shapes in question 5 are made of a square and a triangle.

For the first shape, the side length is 6 units while the side of the triangle is 10 units.

For the second shape, the side length is 5 units while the side of the triangle is x units.

The ratio of the first shape to the second is;

$\frac{6}{5} : \frac{10}{x} , x = (10)(\frac{5}{6} ) = 8.333.$ So $x = 8.333$ units.

6 0

4 years ago

A gym charges a $20 sign-up fee plus $25 per month. You have a $120 gift card for the gym. When does the total spent on your gy

ANEK [815]

4 months........................

3 0

3 years ago

Read 2 more answers

What is 28 percent of 486

Dimas [21]

136.08 hope this helps

5 0

3 years ago

Read 2 more answers

<img src="https://tex.z-dn.net/?f=3%20-%20%20%5Cfrac%7Bx%7D%7B2%7D%20%20%3C%203%20" id="TexFormula1" title="3 - \frac{x}{2} &l

Sergio [31]

The first step for solving this is to cancel equal terms on both sides of the inequality.
$- \frac{x}{2}$ < 0
Now multiply both sides of the inequality by -2 and flip the inequality sign.
-2 × ( $- \frac{x}{2}$ ) > -2 × 0
Remember that multiplying two negatives together always equals a positive,, so the expression changes to the following:
2 × $\frac{x}{2}$ > -2 × 0
Reduce the numbers with 2.
x > -2 × 0
Any expression multiplied by 0 equals 0,, so the correct answer to your question will be:
x > 0
Let me know if you have any further questions.
:)

8 0

4 years ago