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melamori03 [73]
3 years ago
6

A facilities manager at a university reads in a research report that the mean amount of time spent in the shower by an adult is

5 minutes. He decides to collect data to see if the mean amount of time that college students spend in the shower is significantly different from 5 minutes. In a sample of 15 students, he found the average time was 4.29 minutes and the standard deviation was 0.75 minutes. Using this sample information, conduct the appropriate hypothesis test at the 0.01 level of significance. Assume normality.a) What are the appropriate null and alternative hypotheses?H0: ? = 5 versus Ha: ? ? 5H0: x = 5 versus Ha: x ? 5 H0: ? = 5 versus Ha: ? < 5H0: ? = 5 versus Ha: ? > 5b) What is the test statistic? Give your answer to four decimal places. c) What is the P-value for the test? Give your answer to four decimal places. d) What is the appropriate conclusion?
Mathematics
1 answer:
arlik [135]3 years ago
7 0

Answer:

(a) <em>H₀</em>: <em>μ</em> = 5 vs. <em>Hₐ</em>: <em>μ</em> ≠ 5.

(b) The test statistic value is -3.67.

(c) The <em>p</em>-value of the test is 0.0025.

(d) The mean amount of time spent in the shower by an adult is different from 5 minutes.

Step-by-step explanation:

In this case we need to test whether the mean amount of time that college students spend in the shower is significantly different from 5 minutes.

The information provided is:

n=15\\\bar x=4.29\\s=0.75\\\alpha =0.01

(a)

The hypothesis for the test can be defined as follows:

<em>H₀</em>: The mean amount of time spent in the shower by an adult is 5 minutes, i.e. <em>μ</em> = 5.

<em>Hₐ</em>: The mean amount of time spent in the shower by an adult is different from 5 minutes, i.e. <em>μ</em> ≠ 5.

(b)

As the population standard deviation is not known we will use a <em>t</em>-test for single mean.

Compute the test statistic value as follows:

t=\frac{\bar x-\mu}{s/\sqrt{n}}\\\\=\frac{4.29-5}{0.75/\sqrt{15}}\\\\=-3.67

Thus, the test statistic value is -3.67.

(c)

Compute the <em>p</em>-value of the test as follows:

p-value=2\times P(t_{\alpha/2, (n-1)}

*Use a <em>t</em>-table.

Thus, the <em>p</em>-value of the test is 0.0025.

(d)

Decision rule:

If the <em>p</em>-value of the test is less than the significance level then the null hypothesis will be rejected and vice-versa.

<em>p</em>-value = 0.0025 < <em>α</em> = 0.01

The null hypothesis will be rejected at 1% level of significance.

Thus, concluding that the mean amount of time spent in the shower by an adult is different from 5 minutes.

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You measure 47 backpacks' weights, and find they have a mean weight of 79 ounces. Assume the population standard deviation is 13
ki77a [65]

Answer:

3.14

Step-by-step explanation:

Given that:

Mean weight (m) = 79 ounces

Population standard deviation (s) = 13.1

Sample size = 47

Maximal margin of error associated with 90% confidence interval.

The margin of error is given by:

Zcritical * (standard deviation / sqrt(sample size)

Z critical at 90% confidence interval = 1.645

Hence,

Zcritical * (standard deviation / sqrt(sample size)

1.645 * 13.1 / sqrt(47)

1.645 * (13.1 / 6.8556546)

1.645 * 1.9108313

Hence, the margin of error is :

3.1433174885

= 3.14

8 0
3 years ago
Distribute to create an equivalent
seraphim [82]

Answer:

6 - 16y

Step-by-step explanation:

2(3 – 8y) = 2 × 3 - 2 × 8y = 6 - 16y

7 0
1 year ago
50 pts! Fill in the blanks (see attachment for clues necessary to fill blanks).
Alexxx [7]

Hello!

We have the following colors.

red

blue

green

white

yellow

We have the following directions.

North

South

East

West

Center

We also have the following locations.

Cavern Entrance

Bank

Fishing Hole

Fundamental Magic Shop

Sacred Tree

First of all, let's try to match each star with a color.

We see that the fourth star to fall was not a Primary color. This means it was either green or white. Let's look for a reference to green or white to see which one the 4th star is.

We see that neither the white nor green star fell at the bank. Therefore, this star 4 is not at the bank. Let's look at our information on star 4. We see that white fell one of the first three nights. Therefore, star 4 is green.

Star 4

Not at the Bank

Green

As you can see, we don't have any more information quite yet. We do have some information on the red star, though. It did not fall at the cavern entrance, and it was in the constellation for at least 3 days. This means it was either 4 or 5. As we said before, 4 is Green, so Star 5 is red.

Star 5

Red

Did not Fall in the Cavern Entrance

Now, let's see what else we can discover.

The north star fell on an even numbered day. As you can see, this means either the 2nd or the Green star came from the North.

Let's think about locations for a moment. We know that the white or green star did not fall at the bank. We see that the second star to fall landed at either the bank or the Sacred Tree. But, we also see that they West star landed in the Sacred Tree.

Let's also think about directions. The third star to fall was in the center. The center and east stars fell sequentially, so the east star is either the 2nd or 4th star. Before, we said the 2nd of 4th star came from the north. This means that the 1st and 5th stars came from the South or West.

We also see that the blue and yellow stars were on opposite sides of the constellation. We know that the 1st and 2nd stars are blue and yellow due to elimination. We know that the north star fell on an even numbered day, which is either 2 or 4. This means 2 could be either North or East.

We also see that the center star would not have fallen at Fungimental Magic as it was not a cardinal direction.

We also see that the yellow star most likely landed in the fishing whole, as it could have looked like a yellow rock that scared of fish.

Let's think about each of our stars so far.

Star 1

Blue or Yellow

South or West

Could have Fallen at Sacred Tree (could be west)

Could have Landed in Fishing Hole

Star 2

Blue or Yellow

North or East

Bank or Sacred Tree

Star 3

White

Center

Did not fall at Bank

Star 4

Green

North or East

Did not Fall at Bank

Star 5

Red

South or West

Did not Fall at the Bank

Now, let's think of what landed at the bank. We know red and green didn't, and we know that the western one landed in the Sacred Tree. The thing is, we know the yellow one landed in the fishing hole. This means the yellow one is not west. Therefore, the 2nd star is not East, but it is north. This means star 4 is East, and Star 1 is South. This also means the Star 5 is West.

As you can see, we know that the red star fall at the Sacred Tree, so the second star fell at the bank. We can also see that the center star did not fall at the Fundamental Magic Shop. As you can see, the yellow star fell in the fishing hole. As you can see, star 2 landed at the bank, so star 1 is yellow and star 2 is blue.

If we do so, all we need to discover is the locations of star 3 and 4. We know that 3 did not fall at the Fundamental Magic, so that means 4 did so. This means 3 fell at the Cavern entrance.

Star 1: South, Yellow, Fishing Hole

Star 2: North, Bank, Blue,

Star 3: Center, White, Cavern Entrance

Star 4: East, Green, Fundamental Magic

Star 5: West, Sacred Tree, Red,

Therefore, our answers are shown below.

---------------------------------------------------------------

The 1st star was yellow, came from the South, and fell into the fishing hole.

The 2nd star was blue, came from the North, and fell into the bank.

The 3rd star was white, came from the center, and fell into the Cavern Entrance.

The 4th star was green, came from the East, and landed in Fundamental Magic.

The 5th star was red, came from the West, and fell into the Sacred Tree.

I hope this helps!

3 0
3 years ago
A die is rolled. Find the probability of the given event. (a) The number showing is a 2; The probability is : (b) The number sho
Sphinxa [80]

Answer:

(a) 1/6

(b) 1/2

(c) 1/3

Step-by-step explanation:

There are 6 possible outcomes.

(a) The number is 2: only 1 outcome out of 6, hence 1/6

(b) The number is even: {2, 4, 6} - 3 outcomes out of 6, hence 3/6 = 1/2

(c) The number is greater than four: {5, 6} - 2 outcomes out of 6, hence 2/6 = 1/3

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vaieri [72.5K]
It looks like the measure would be 97 or 93 I think
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