MATHEMATICS COLLEGE

The time needed for all college students to complete a certain paper-and-pencil maze follows a normal distribution with a population mean of 30 seconds and a population standard deviation of 3 seconds. You wish to see if the mean time μ (where μ stands for population mean) is changed by vigorous exercise, so you have a group of nine college students exercise vigorously for 30 minutes and then complete the maze. It takes them an sample average of 31.2 seconds to complete the maze. Use this information to test the hypotheses:

H0: μ = 30,

Ha: ≠30

at the significance level of 0.01.

You conclude:

a) There is not enough evidence to support the claim.

b) There is enough evidence to support the claim.

Answers

Answer 1

Answer:

The correct option is a

Step-by-step explanation:

From the question we are told that

The population mean is $\mu = 30\ seconds$

The standard deviation is $\sigma = 3 \ seconds$

The sample size is n = 9

The null hypothesis is $H_o: \mu = 30$

The alternative hypothesis is $H_a : \mu \ne 30$

The level of significance is $\alpha = 0.01$

The sample mean is $\= x = 31.2$

Generally the test statistics is mathematically represented as

$z = ( \= x - \mu )/( (\sigma)/(√(n) ) )$

=> $z = ( 31.2 - 30)/( (3)/(√(9) ) )$

=> $z = 1.2$

From the z table the area under the normal curve to the right corresponding to 1.2 is

$P(Z > 1.2) = 0.11507$

Generally the p-value is mathematically represented as

$p-value = 2 * P(Z > 1.2)$

=> $p-value = 2 *0.11507$

=> $p-value = 0.230$

From the value obtained w can see that

$p-value > \alpha$ hence

The decision rule is

Fail to reject the null hypothesis

The conclusion is there is not enough evidence to support the claim

Answer 2

Answer:

Final answer:

To test the hypotheses, use a one-sample t-test to compare the sample mean to the population mean. Calculate the t-value and compare it to the critical t-value at the significance level of 0.01. If the calculated t-value falls within the critical region, reject the null hypothesis. Otherwise, fail to reject the null hypothesis.

Explanation:

To test the hypotheses, we can use a one-sample t-test since we know the population standard deviation and the sample size is small. The null hypothesis (H0) is that the population mean (μ) is equal to 30 seconds, while the alternative hypothesis (Ha) is that the population mean is not equal to 30 seconds.

Using the given information, we can calculate the t-value by using the formula:

t = (sample mean - population mean) / (population standard deviation / sqrt(sample size))

Once we have the t-value, we can compare it to the critical t-value at the significance level of 0.01. If the calculated t-value falls within the critical region, we reject the null hypothesis. If not, we fail to reject the null hypothesis and conclude that there is not enough evidence to support the claim.

Learn more about Hypothesis testing here:

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There were 2,626,418 deaths in 2014 according to the CDC. 614,348 of these deaths were caused by diseases of the heart and 136,053 were caused by unintentional injuries. What is the probability that a death in 2014 was not caused by diseases of the heart or unintentional injuries

Answers

Answer:

= 0.714 (in decimal fraction)

The probability that the death in 2014 was not caused by heart diseases or Unintentional Injuries = 0.714

= 0.714

Step-by-step explanation:

Let's interpret the question our way ti solve it .

Total deaths in 2014:

2626418

Death caused by Heart Diseases:

614348

Death caused by Unintentional Injuries:

750401

Therefore, we can deduced that, the number of death not caused by Heart Diseases or Unintentional Injuries = Total deaths in 2014 minus sum of the recorded death.

= 2626418 - ( 614348 + 136053)

= 2626418 - 750401

= 1876017.

Now, the probability that there were death in 2014 is 1 (one)

To find the probability that death we're not caused by heart diseases or Unintentional Injuries:

= 1 - Pr (Death Caused by heart diseases) + Pr (Death causes by Unintentional Injuries)

= 1 - (0.234 + 0.052)

= 1 - 0.286

= 0.714

To Check:

= 1876017 / 2626418

Divide to the lowest term

=0.714

The probability that a death in 2014 was not caused by diseases of the heart or unintentional injuries is approximately 0.714 or 71.4%.

Here, we have to find the probability that a death in 2014 was not caused by diseases of the heart or unintentional injuries, we need to subtract the number of deaths caused by these two specific causes from the total number of deaths and then divide it by the total number of deaths.

Total number of deaths in 2014: 2,626,418

Number of deaths caused by diseases of the heart: 614,348

Number of deaths caused by unintentional injuries: 136,053

Number of deaths not caused by diseases of the heart or unintentional injuries = Total deaths - Deaths caused by diseases of the heart - Deaths caused by unintentional injuries

Number of deaths not caused by diseases of the heart or unintentional injuries = 2,626,418 - 614,348 - 136,053

Number of deaths not caused by diseases of the heart or unintentional injuries = 1,876,017

Now, we can calculate the probability:

Probability = Number of deaths not caused by diseases of the heart or unintentional injuries / Total number of deaths

Probability = 1,876,017 / 2,626,418

Probability ≈ 0.714 (rounded to three decimal places)

So, the probability that a death in 2014 was not caused by diseases of the heart or unintentional injuries is approximately 0.714 or 71.4%.

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Quan likes to exercise by running every day. On average, he runs 5 miles each day. This varies by about 0.3 mile. What are the maximum and minimum numbers of miles Quan is expected to run each day?

Answers

Answer:

Quan runs a maximum of 5.3 miles and a minimum of 4.7 miles every day.

Step-by-step explanation:

Let x= the actual measurement.

|actual − ideal|≤ tolerance

Use an absolute value inequality to express this situation.

|x−5|≤0.3

Rewrite as a compound inequality.

−0.3≤x−5≤0.3

Solve the inequality.

4.7≤x≤5.3

Answer the question. Quan runs a maximum of 5.3 miles and a minimum of 4.7 miles every day.

In one city, the ratio of households with pets tohouseholds without pets is 30 to 29. If 20,735 households
do not have pets, how many households have pets?
A 21.450
B 42,185
C 40,779
D 20.044

Answers

Answer:

40,779

Step-by-step explanation:

i took the k12 test

Find the area of the triangle Please help

Answers

Answer:

14m^2

Step-by-step explanation:

Area of a triangle is - 1/2 base times hight

two triangels find the srea of both and add them

4x4x1/2 = 16x1/2 = 8m

3x4x1/2 = 12x1/2 = 6m

6m + 8m = 14m

Match the correct y=mx+b equation to the graph:

pls show work/explanation!

Answers

Answer:

$y=-3x+2$

$\boxed{m=-3,\ b=2}$

Step-by-step explanation:

Equation of a line

To define the equation of a line, we only need two points through which it passes. The graph shows two clear points to choose: (0,2) and (1,-1)

Set up the equation of the line by using the formula

$\displaystyle y-y_1=(y_2-y_1)/(x_2-x_1)(x-x_1)$

$\displaystyle y-2=(-1-2)/(1-0)(x-0)$

Operating

$y-2=-3x$

Rearranging

$y=-3x+2$

$\boxed{m=-3,\ b=2}$

Which best describes how to find an equation of the line shown?A. The slope m is rise over run, so y over x =m. Solve for Y to get y=mx.

B. The slope m is run over rise, so x over y=m. Solve for x=ym.

C. The slope m is run over rise, so x over y=m. Solve for y to get y= x over m.

D. The slope m is rise over run, so x over y=m. Solve for x to get x=ym.

Answers

Answer:

A

Step-by-step explanation:

m (slope) = rise = y = y₁ - y₁

run x x₁ - x₁

to get y = mx

therefore, the answer to the question is :

A. The slope m is rise over run, so y over x =m.

Solve for y to get y=mx.

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