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health insurance plan
/in Questions Uploads /by Hannah WanguiQuestion
Let x be the average number of employees in a group health insurance plan, and let y be the
average administrative cost as a percentage of claims.
x
3
7
15
36
70
y
40
35
30
27
16
(a) Make a scatter diagram of the data and visualize the line you think best fits the data.
(b) Would you say the correlation is low, moderate, or strong? positive or negative?
strong and positive moderate and negative moderate and positive low and positive strong and negative low and negative
(c) Use a calculator to verify that Σx = 131, Σx2 = 6479, Σy = 148, Σy2 = 4710, and Σxy = 2907. Compute r. (Round your answer to three decimal places.)
r =
As x increases, does the value of r imply that y should tend to increase or decrease? Explain.
Given our value of r, y should tend to increase as x increases. Given our value of r, y should tend to decrease as x increases. Given our value of r, we cannot draw any conclusions for the behavior of y as x increases. Given our value of r, y should tend to remain constant as x increases.
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Using time value of money
/in Questions Uploads /by Hannah WanguiQuestion
Using time value of money (your financial calculator or Excel including inputs). I
can only put away $2,000 a year toward retirement. I am 25 and plan on retiring at 65 and earning 5%. How much will I have at retirement?
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A new thermostat
/in Questions Uploads /by Hannah WanguiQuestion
A new thermostat has been engineered for the frozen food cases in large supermarkets. Both the old and new
thermostats hold temperatures at an average of 25°F. However, it is hoped that the new thermostat might be more dependable in the sense that it will hold temperatures closer to 25°F. One frozen food case was equipped with the new thermostat, and a random sample of 26 temperature readings gave a sample variance of 4.7. Another similar frozen food case was equipped with the old thermostat, and a random sample of 15 temperature readings gave a sample variance of 12.8. Test the claim that the population variance of the old thermostat temperature readings is larger than that for the new thermostat. Use a 5% level of significance. How could your test conclusion relate to the question regarding the dependability of the temperature readings? (Let population 1 refer to data from the old thermostat.)
(a) What is the level of significance?
State the null and alternate hypotheses.
H0: σ12 = σ22; H1: σ12 < σ22H0: σ12 > σ22; H1: σ12 = σ22 H0: σ12 = σ22; H1: σ12 > σ22H0: σ12 = σ22; H1: σ12 ≠ σ22
(b) Find the value of the sample F statistic. (Round your answer to two decimal places.)
What are the degrees of freedom?
dfN
=
dfD
=
What assumptions are you making about the original distribution?
The populations follow independent normal distributions. We have random samples from each population. The populations follow independent chi-square distributions. We have random samples from each population. The populations follow dependent normal distributions. We have random samples from each population. The populations follow independent normal distributions.
(c) Find or estimate the P-value of the sample test statistic. (Round your answer to four decimal places.)
p-value > 0.100 0.050 < p-value < 0.100 0.025 < p-value < 0.050 0.010 < p-value < 0.025 0.001 < p-value < 0.010 p-value < 0.001
(d) Based on your answers in parts (a) to (c), will you reject or fail to reject the null hypothesis?
At the α = 0.05 level, we fail to reject the null hypothesis and conclude the data are not statistically significant. At the α = 0.05 level, we reject the null hypothesis and conclude the data are not statistically significant. At the α = 0.05 level, we fail to reject the null hypothesis and conclude the data are statistically significant. At the α = 0.05 level, we reject the null hypothesis and conclude the data are statistically significant.
(e) Interpret your conclusion in the context of the application.
Reject the null hypothesis, there is sufficient evidence that the population variance is larger in the old thermostat temperature readings. Reject the null hypothesis, there is insufficient evidence that the population variance is larger in the old thermostat temperature readings. Fail to reject the null hypothesis, there is sufficient evidence that the population variance is larger in the old thermostat temperature readings. Fail to reject the null hypothesis, there is insufficient evidence that the population variance is larger in the old thermostat temperature readings.
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