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
denis23 [38]
3 years ago
10

A well-known brokerage firm executive claimed that 60% of investors are currently confident of meeting their investment goals. A

n XYZ Investor Optimism Survey, conducted over a two week period, found that in a sample of 100 people, 69% of them said they are confident of meeting their goals. Test the claim that the proportion of people who are confident is larger than 60% at the 0.01 significance level.
The null and alternative hypothesis would be:________
a. H0:μ=0.6H0:μ=0.6
H1:μ≠0.6H1:μ≠0.6
b. H0:μ=0.6H0:μ=0.6
H1:μ<0.6H1:μ<0.6
c. H0:μ=0.6H0:μ=0.6
H1:μ>0.6H1:μ>0.6
d. H0:p=0.6H0:p=0.6
H1:p≠0.6H1:p≠0.6
e. H0:p=0.6H0:p=0.6
H1:p>0.6H1:p>0.6
f. H0:p=0.6H0:p=0.6
H1:p<0.6H1:p<0.6
The test is:________
a. two-tailed
b. left-tailed
c. right-tailed
The test statistic is:_______ (to 3 decimals)
The p-value is:_______ (to 4 decimals)
Based on this we:________
a. Fail to reject the null hypothesis
b. Reject the null hypothesis
Mathematics
1 answer:
mojhsa [17]3 years ago
7 0

We are testing a hypothesis. So, first we identify the null and the alternative hypothesis, then we find the test statistic, and with the test statistic, the p-value is found.

Null and alternative hypothesis:

Claim the the proportion is of 60%, thus, the null hypothesis is:

H_0: p = 0.6

Test if the proportion is greater than 60%, thus, the alternative hypothesis is:

H_1: p > 0.6

And the answer to the first question is given by option c.

Classification:

We are testing if the proportion is greater than a value, so it is a right-tailed test.

Test statistic:

z = \frac{X - \mu}{\frac{\sigma}{\sqrt{n}}}

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

0.6 is tested at the null hypothesis:

This means that \mu = 0.6, \sigma = \sqrt{0.4*0.6}

Survey, conducted over a two week period, found that in a sample of 100 people, 69% of them said they are confident of meeting their goals.

This means that n = 100, X = 0.69

Value of the test statistic:

z = \frac{X - \mu}{\frac{\sigma}{\sqrt{n}}}

z = \frac{0.69 - 0.6}{\frac{\sqrt{0.4*0.6}}{\sqrt{100}}}

z = 1.837

The test statistic is z = 1.837.

p-value:

The p-value of the test is the probability of finding a sample proportion above 0.69, which is 1 subtracted by the p-value of z = 1.837.

Looking at the z-table, z = 1.837 has a p-value of 0.9669.

1 - 0.9669 = 0.0331

The p-value is 0.0331.

Decision:

The p-value of the test is 0.0331 > 0.01, and thus:

a. Fail to reject the null hypothesis

For another example of a problem of a test of hypothesis, you can take a look at:

brainly.com/question/24166849

You might be interested in
Matt had a full jar of marbles. He gave Kayla 3/4 of the marbles. Then Kayla returned 1/3 of a jar's worth of marbles to the jar
Aleks [24]
Full jar of marbles, <span>He gave Kayla 3/4 of the marbles so 1/4 left
</span><span>Then Kayla returned 1/3 of a jar's worth of marbles to the jar

1/4 + 1/3 = 3/12 + 4/12 = 7/12

Answer: 7/12 jar of marbles now.</span>
8 0
3 years ago
Read 2 more answers
Find the area of the shaded regions
Salsk061 [2.6K]

your answer would be 254 I just did it and I got it right ✨

4 0
2 years ago
Solve these problems not give tips solve
Norma-Jean [14]
The correct answer is "please"
5 0
3 years ago
Read 2 more answers
A deck is in the shape of a square. The area of the deck is 576 swuare feet. which is the length of each side of the deck
NNADVOKAT [17]
A) 24

All side lengths of a square are equal so you take the square root of 576 to get two 24. If you try it back: 24*24 (w*h) to get 576.
7 0
2 years ago
Read 2 more answers
Help Please Will Give Brainliest
il63 [147K]
31 I think I’m not sure may be wrong
7 0
3 years ago
Read 2 more answers
Other questions:
  •  Amy​'s car holds at most 19 gallons of gas. Now it has 9 gallons. Use pencil and paper. Explain how to find the amount of gas s
    9·1 answer
  • Which of the relations has a domain of {-5, 0, 5}?
    8·2 answers
  • Find the product. 4(−12)(−3) A) −144 B) −96 C) 144 D) 72
    9·1 answer
  • If a line passes through the point (0,-8), the y-intercept is
    6·1 answer
  • Students in a fitness class each completed a one-mile walk or run. The list shows the time it took each person to complete the m
    11·2 answers
  • A rule was used to create this list of points. Is the rule a function or not a function?
    7·1 answer
  • Mary bought a circular rug for the living room. The rug has a radius of 16 feet. Which measurement is closest to the circumferen
    15·1 answer
  • For the following function, evaluate f(2): f(x) = |x - 8| + 2​
    9·2 answers
  • Please someone help me quickly
    7·1 answer
  • Please answer both questions! I know that there are answers in the boxes but I’m not sure if they are correct.
    11·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!