A cell phone company states that the mean cell phone bill of all their customers is less than $83. A sample of 19 customers gives a sample mean bill of $82.17 and a sample standard deviation of $2.37. At ? = 0.05 , test the company’s claim?
1). State the hypothesis and label which represents the claim: : H 0 : H a
2). Specify the level of significance =
3). Sketch the appropriate distribution, find and label the Critical Value(s) in Statdisk to 3 decimal places, and shade in to indicate the Rejection Region(s)
4.) Calculate the test statistic (to 3 decimal places). Label this appropriately as Z or t.
5). Decision: Reject Ho or Do Not Reject Ho (You do not have to write a statement):
6). In the distribution below, label the test statistic you calculated from part (4). Using Statdisk, find the P-value corresponding to the test statistic. Shade in and label the P-value in the distribution.
In: Statistics and Probability
The company who makes Chips Ahoy cookies states that there is an average of 23 chocolate chips per cookie. You take a sample of cookies and count the chips. For your sample of 30 cookies, the average # of chips in the cookies is 23.6 chips with a standard deviation of 2 chips. Use this data to test the claim that the company makes. Use a 95% significance level but you may use a two tailed OR a one tailed test. You decide. Does your hypothesis test support the claim that Chip Ahoy is making?
Provide a 95% confidence interval to estimate the true number of chips in Chips Ahoy cookies. Does your interval support the claim of the company?
In: Statistics and Probability
A (time-homogeneous) Markov chain built on states A and B is depicted in the diagram below. What is the probability that a process beginning on A will be on B after 2 moves?
consider the Markov chain shown in Figure 11.14.
Figure 11.14- A state transition diagram.
In: Statistics and Probability
A recent publication states that the average closing cost for
purchasing a new home is $8586. A real estate agent believes the
average closing cost is more than $8586. She selects 28 new home
purchases and finds that the average closing costs are $8582 with a
standard deviation of $341. Help her decide if she is correct by
testing her claim at αα=0.01.
The correct hypotheses would be:
Since the level of significance is 0.01 the critical value is
2.473
The test statistic is: (round to 3 places)
The p-value is: (round to 3 places)
The decision can be made to:
The final conclusion is that:
A new baker is trying to decide if he has an appropriate price
set for his 3 tier wedding cakes which he sells for $84.68. He is
particullarly interested in seeing if his wedding cakes sell for
less than the average price. He searches online and finds 23 of the
competitors in his area that sell 3 tier wedding cakes with a mean
price of $87.73 with a standard deviation of $6.19. Help the new
baker by testing his his claim with a 0.10 level of
significance.
The correct hypotheses would be:
Since the level of significance is 0.10 the critical value is
1.321
The test statistic is: (round to 3 places)
The p-value is: (round to 3 places)
The decision can be made to:
The final conclusion is that:
In: Statistics and Probability
Two states of nature exist for a particular situation: a good economy and a poor economy. An economic study may be performed to obtain more information about which of these will actually occur in the coming year. The study may forecast either a good economy or a poor economy. Currently there is a 60% chance that the economy will be good and a 40% chance that it will be poor. In the past, when ever the economy was good, the economic study predicted it would be good 80% of the time. (The other 20% of the time the prediction was wrong.) In the past, whenever the economy was poor, the economic study predicted it would be poor 90% of the time. (The other 10% of the time the prediction was wrong.)
(A) Use Bayes’ theorem and find the following:
P (good economy | prediction of good economy)
P (poor economy | prediction of good economy)
P (good economy | prediction of poor economy)
P (poor economy | prediction of poor economy)
(B) Suppose the initial (prior) probability of a good economy is 70% (instead of 60%), and the probability of a poor economy is 30% (instead of 40%). Find the posterior probabilities in part a
based on these new values.
In: Statistics and Probability
Mid States Company is a regional chain department store. It will
remain in business for one more year. The probability of a boom
year is 60 percent and the probability of a recession is 40
percent. It is projected that the company will generate a total
cash flow of $188 million in a boom year and $79 million in a
recession. The company's required debt payment at the end of the
year is $113 million. The market value of the company’s outstanding
debt is $86 million. The company pays no taxes.
a. What payoff do bondholders expect to receive in
the event of a recession? (Do not round intermediate
calculations. Enter your answer in dollars, not millions of
dollars, e.g. 1,234,567.)
Payoff
$
b. What is the promised return on the company's
debt? (Do not round intermediate calculations. Enter your
answer as a percent rounded to 2 decimal places, e.g.,
32.16.)
Promised return
%
c. What is the expected return on the company's
debt? (Do not round intermediate calculations. Enter your
answer as a percent rounded to 2 decimal places, e.g.,
32.16.)
Expected return
%
In: Finance
The following is the transition probability matrix of a Markov chain with states 1, 2, 3, 4 P
| 0 | 1 | 2 | 3 | |
|---|---|---|---|---|
| 0 | .4 | .3 | .2 | .1 |
| 1 | .2 | .2 | .2 | .4 |
| 2 | .25 | .25 | .5 | 0 |
| 3 | .2 | .1 | .4 | .3 |
If Xnot = 1
(a) find the probability that state 3 is entered before state
4;
(b) find the mean number of transitions until either state 3 or
state 4 is entered.
In: Statistics and Probability
The Merck Manual states that, for healthy adults, the mean number of milliliters of oxygen per deciliter of blood is 19.0. A company that sells vitamins claims that its multivitamin complex will increase the oxygen capacity of the blood. A random sample of 28 adults took the vitamin for six months. After blood tests, it was found that the sample mean was 20.7 ml of oxygen per deciliter of blood with a standard deviation of 6.7ml.
a. At the 0.05 level, test the claim that the average oxygen capacity has increased.
b. How much power do you have to detect a 3ml difference (from the null) in the average amount of oxygen in the blood?
c. What sample size would you need to have 90% power to detect this observed difference?
In: Math
6.
Open the PhET States of Matter Simulation to answer the following questions:
(a) Select the Solid, Liquid, Gas tab. Explore by selecting different substances, heating and cooling the systems, and changing the state. What similarities do you notice between the four substances for each phase (solid, liquid, gas)? What differences do you notice?
(b) For each substance, select each of the states and record the given temperatures. How do the given temperatures for each state correlate with the strengths of their intermolecular attractions? Explain.
(c) Select the Interaction Potential tab, and use the default neon atoms. Move the Ne atom on the right and observe how the potential energy changes. Select the Total Force button, and move the Ne atom as before. When is the total force on each atom attractive and large enough to matter? Then select the Component Forces button, and move the Ne atom. When do the attractive (van der Waals) and repulsive (electron overlap) forces balance? How does this relate to the potential energy versus the distance between atoms graph? Explain.
In: Chemistry
A report states the average rent for office space in a urban area is $17.75 per square foot. A real estate agent claims this average is incorrect. The agent selected a sample of 26 rental properties and found their mean to be $19.25 per square foot, with a sample standard deviation of $3.55 per square foot. Test the claim at alpha = 0.10. Use the P-value method to evaluate/compare with the given alpha (0.10
In: Math