1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
bixtya [17]
3 years ago
6

A recent survey by nerdwallet indicated Americans paid a mean of $6,658 interest on credit card debt in 2017. A sample of 12 hou

seholds with children revealed the following amounts. 7,077 5,744 6,753 7,381 7,625 6,636 7,164 7,348 8,060 5,848 9,275 7,052 Click here for the Excel Data File State the null hypothesis and the alternate hypothesis. State the decision rule for 0.05 significance level. (Round your answer to 3 decimal places.) Compute the value of the test statistic. (Round your answer to 3 decimal places.) Is it reasonable to conclude that these households paid more interest than the survey result
Mathematics
1 answer:
mixas84 [53]3 years ago
5 0

Answer:

The null hypothesis is H_0: \mu = 6658

Tha alternate hypothesis is H_a: \mu > 6658

The decision rule is that if t < 1.976, the null hypothesis is not rejected, that is, there is no evidence to conclude that these households paid more interest than the survey result, and that if t > 1.976, the null hypothesis is reject and there is evidence to conclude that these households paid more interest than the survey result.

The test statistic is t = 1.94

As the test statistic of t = 1.94 is higher than the critical value of t, it is reasonable to conclude that these households paid more interest than the survey result

Step-by-step explanation:

A recent survey by nerdwallet indicated Americans paid a mean of $6,658 interest on credit card debt in 2017. Test if it is reasonable to conclude that these households paid more interest than the survey result.

At the null hypothesis, we test if they paid the same, that is:

H_0: \mu = 6658

At the alternate hypothesis, we test if they paid more, that is:

H_a: \mu > 6658

Test statistic:

The test statistic is:

t = \frac{X - \mu}{\frac{s}{\sqrt{n}}}

In which X is the sample mean, \mu is the value tested at the null hypothesis, s is the standard deviation of the sample and n is the size of the sample.

State the decision rule for 0.05 significance level.

Right-tailed test(test if the mean is higher than the value) with 12 - 1 = 11 degrees of freedom, has a critical value of t = 1.976.

So

The decision rule is that if t < 1.976, the null hypothesis is not rejected, that is, there is no reasonable evidence to conclude that these households paid more interest than the survey result, and that if t > 1.976, the null hypothesis is reject and there is reasonable evidence to conclude that these households paid more interest than the survey result.

6658 is tested at the null hypothesis:

This means that \mu = 6658

Sample mean and standard deviation:

With the given data-set:

Mean of X = 7163.6

Standard deviation of s = 902.25

Sample of 12:

This means that n = 12

Compute the value of the test statistic.

t = \frac{X - \mu}{\frac{s}{\sqrt{n}}}

t = \frac{7163.6 - 6658}{\frac{902.25}{\sqrt{12}}}

t = 1.94

As the test statistic of t = 1.94 is higher than the critical value of t, it is reasonable to conclude that these households paid more interest than the survey result

You might be interested in
The sum of two consecutive even numbers is 206. What is the value of the smallest number?
lesya692 [45]

Answer:

102

Step-by-step explanation:

Since we know that the numbers are two consecutive even numbers, we can write an equation like this where n represents the 2 numbers.

n + (n+2) = 206

Simplify the left side:

n + (n+2) = 206 -----> 2n+2 = 206

Subtract 2 from both sides:

2n = 206-2 -----> 2n = 204

Now divide 204 by 2:

n = 204/2 -----> n = 102

3 0
3 years ago
12. A shoebox has a volume of 456 cm3 and a mass of 114 g. What is its<br> density?
victus00 [196]

Answer:

114.0g/538.5cm^3=0.2117 glcm^3

Step-by-step explanation:

8 0
3 years ago
2. The line that passes through the points (-6, p)
Kobotan [32]
Answer: -26=p


Explanation: The slope formula is m=(y2-y1)/(x2-x1).

Thus, we have 6=(2-p)/(-10-(-6)).

Combining the xs gives us 6=(2-p)/-4.

Multiplying both sides by -4 leaves us with -24=2-p.

We do -24-2 to isolate p and find that p=-26.
5 0
3 years ago
Father says my son is five times older than my daughter. my wife is 5 times older that my son. I am twice old from my wife and a
Svet_ta [14]

Answer:

daughter 1. son 5. wife 25. father 50

4 0
3 years ago
Study the geometric sequence {-4, -84, -1764, -37044, ...}.
Nonamiya [84]

Answer:

              \bold{a_n=(-4)21^{n-1}}

Step-by-step explanation:

a_1=-4\,,\ a_2=-84\,,\ a_3=-1764\,,\ a_4=-37044\quad\implies\ \ r=21

{-84:(-4)=21 and -1764:(-84)=21 and -37044:(-1764)=21}

geometric sequence formula:   a_n=a_1r^{n-1}

a_1=-4\quad and \ \ r=21

a_n=(-4)21^{n-1}

3 0
3 years ago
Other questions:
  • How do I find x in this equation?
    10·1 answer
  • -10y + 18 = -3 (5y - 7) + 5y
    14·1 answer
  • Convert the angle O= 35° to radians.<br> Express your answer exactly.<br> radians
    10·1 answer
  • Find the probability of rolling divisors of 24
    11·1 answer
  • Another question ...
    9·2 answers
  • In ΔKLM, the measure of ∠M=90°, the measure of ∠K=75°, and LM = 6.3 feet. Find the length of KL to the nearest tenth of a foot.
    5·2 answers
  • At the end of the year, Close made the current year on mark down to make Room for next year models. One particular model had a s
    7·1 answer
  • Which of the following are quadrilaterals?
    6·2 answers
  • Determine the unknown side lengths.<br><br> X= ?<br><br> Y= ?
    9·2 answers
  • Factor completely the polynomial xy+2y-2x-4? please solve asap.
    5·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!