checking answers and solving 4 more

Anonymous
timer Asked: Dec 14th, 2018
account_balance_wallet $15

Question description

I have the first document for Quiz2 where i have stated answers but not fully sure of them, or if i answered all parts of the equation. So I would like you to go over them and check them again and complete whats missing.

the next document contain 4 questions only i would like you so solve them please

thank you.

Math 260 Quiz 2 Name: ____________________ Problem 1 Is there a difference in average miles traveled for each of two taxi companies during a randomly selected week? The data are: Yellow Cab Company American United Company X1=837 X2=753 σ =30 σ =40 n1=35 n2=40 Use α= 0.05. assume that the populations are normally distributed. a. State the null Hypothesis. b. State the alternative hypothesis. c. Is this a right-tailed test, Left-tailed, or a two-tailed test? d. Which statistical distribution applies for this problem? e. Find the critical values? Show the critical values on the graph of the distribution, and identify the rejection region and non-rejection region f. Compute the test values. g. Make your decision based the test vales and the critical values. h. Summarize the results. 1 Math 260 Quiz 2 Name: ____________________ Problem 2 Two brands of batteries are tested, and their voltages are compared. The summary statistics follow. Find the 95% confidence interval of the true difference in the means. Assume that both variables are normally distributed. Exercise: Battery Voltage Brand X Brand Y Problem 3 The number of murders and robberies per 100,000 population for a random selection of states is shown. Is there a linear relationship between the variables? Murders 2.4 2.7 Robberies 25.3 14.3 5.6 2.6 2.1 3.3 6.6 151.6 91.1 80 49 173 5.7 95.8 a. Draw the scatter plot for the variables. b. Compute the value of the correlation coefficient. c. State the hypotheses. d. Test the significance of the correlation coefficient at α = 0.05, using Table I. e. Give a brief explanation of the type of relationship. Assume all assumptions have been met. 2 Math 260 Quiz 2 Name: ____________________ Problem 4 A physician wishes to know whether there is a relationship between a father's weight (in pounds) and his newborn son's weight (in pounds). The data are given here. Father's weight x 176 Son's weight y 6.6 160 8.2 187 9.2 210 7.1 196 8.8 142 9.3 205 7.4 215 8.6 a. Draw a scatter plot. b. Compute the correlation coefficient. c. State the hypotheses. d. Test the hypotheses at α = 0.05. Use Table I. e. Determine the regression line equation if r is significant. f. Plot the regression line on the scatter plot, if appropriate. g. Summarize the results. 3
Math 260 Quiz 2 Name: ____________________ Problem 1 Is there a difference in average miles traveled for each of two taxi companies during a randomly selected week? The data are: Yellow Cab Company American United Company X1=837 X2=753 σ =30 σ =40 n1=35 n2=40 Use α= 0.05. assume that the populations are normally distributed. a. State the null Hypothesis. b. State the alternative hypothesis. c. Is this a right-tailed test, Left-tailed, or a two-tailed test? d. Which statistical distribution applies for this problem? e. Find the critical values? Show the critical values on the graph of the distribution, and identify the rejection region and non-rejection region f. Compute the test values. g. Make your decision based the test vales and the critical values. h. Summarize the results. 1 Math 260 Quiz 2 Name: ____________________ Problem 2 Two brands of batteries are tested, and their voltages are compared. The summary statistics follow. Find the 95% confidence interval of the true difference in the means. Assume that both variables are normally distributed. Exercise: Battery Voltage Brand X Brand Y Problem 3 The number of murders and robberies per 100,000 population for a random selection of states is shown. Is there a linear relationship between the variables? Murders 2.4 2.7 Robberies 25.3 14.3 5.6 2.6 2.1 3.3 6.6 151.6 91.1 80 49 173 5.7 95.8 a. Draw the scatter plot for the variables. b. Compute the value of the correlation coefficient. c. State the hypotheses. d. Test the significance of the correlation coefficient at α = 0.05, using Table I. e. Give a brief explanation of the type of relationship. Assume all assumptions have been met. 2 Math 260 Quiz 2 Name: ____________________ Problem 4 A physician wishes to know whether there is a relationship between a father's weight (in pounds) and his newborn son's weight (in pounds). The data are given here. Father's weight x 176 Son's weight y 6.6 160 8.2 187 9.2 210 7.1 196 8.8 142 9.3 205 7.4 215 8.6 a. Draw a scatter plot. b. Compute the correlation coefficient. c. State the hypotheses. d. Test the hypotheses at α = 0.05. Use Table I. e. Determine the regression line equation if r is significant. f. Plot the regression line on the scatter plot, if appropriate. g. Summarize the results. 3
Math 260 Quiz 2 Name: ____________________ ===================================================================================== Problem 1 A meteorologist who sampled 13 thunderstorms found that the average speed at which they traveled across a certain state was 15 mikes per hour. The standard deviation of the sample was 1.7 miles per hour. a. What is the parameter of interest? b. What is alpha? c. Which statistical distribution applies for this problem? d. Calculate the error? E=Zα/2 (Ϭ/sqrt(n)) e. Find a 99% confidence interval of the mean. f. If a meteorologist wanted to use the highest speed to predict the times it would take storms to travel across the state in order to issue warnings, what figure would she likely use? 1 Math 260 Quiz 2 Name: ____________________ ===================================================================================== Problem 2 A pizza shop owner wishes to find the 95% confidence interval of the true mean cost of a large pizza. How large should the sample be if he wishes to be accurate to within $0.15? A previous study showed the standard deviation of the price was $0.26. Solution: n = (z*s/E)^2 n = (1.96*0.26/0.15)^2 n = 11.5 n = 12 Problem 3 A researcher reports that the average salary of assistant professors is more than $42,000. A sample of 30 assistant professors has a mean salary of $43,260. At α = 0.01, test the claim that assistant professors earn more than $42,000 a year. The standard deviation of the population is $5230. a. What is the parameter of interest? b. State the null Hypothesis. c. State the alternative hypothesis. d. Is this a right-tailed test, Left-tailed, or a two-tailed test? e. Which statistical distribution applies for this problem? 2 Math 260 Quiz 2 Name: ____________________ ===================================================================================== f. Find the critical values? Show the critical values on the graph of the distribution, and identify the rejection region and non-rejection region g. Compute the test values. h. Make your decision based the test vales and the critical values. i. Summarize the results. j. Is this a type one error or Type two error? Solution: Step 1: State the hypotheses and identify the claim. Null Hypotheses (H0): µ = $42,00 and Alternative Hypotheses (H1): µ > $42,000 (claim) Step 2: Find the critical value. Since a=0.05 and the test is a right-tailed test, the critical value is z=1.65. Step 3: Compute the test value. Step 4: Make the decision. Since the test value, 1.32 is less than the critical value 1.65, and is not in the critical region, the decision is “Do not reject the null hypothesis”. Step 5: Summarize the results. There is not enough evidence to support the claim that assistant professors earns more on average than $42,000 a year. Even though the sample mean, $43,000, is higher than the hypothesized population mean of $42,000, it is not significantly higher. Hence, the difference may due to chance. It should be noted that when the null hypothesis is not rejected, it cannot be accepted as true. There is merely not enough evidence to say that it is false. This guideline may sound a little confusing, but the situation is analogous to a jury trial. The verdict is either guilty or not guilty and is based on the evidence presented. If a person is judged not guilty, it does not mean that the person is proved innocent; it only means that there is enough evidence to reach the guilty verdict. Problem 4 A large university reports that the mean salary of parents of an entering class is $91,600. To see how this compares to his university, a president surveys 28 randomly selected families and finds that their average income is $88,500. If the standard deviation is $10,000, can the president conclude that there is a difference? At α= .05, is he correct? a. What is the parameter of interest? 3 Math 260 Quiz 2 Name: ____________________ ===================================================================================== b. State the null Hypothesis. c. State the alternative hypothesis. d. Is this a right-tailed test, Left-tailed, or a two-tailed test? e. Which statistical distribution applies for this problem? f. Find the critical values? Show the critical values on the graph of the distribution, and identify the rejection region and non-rejection region g. Compute the test values. h. Make your decision based the test vales and the critical values. i. Summarize the results. j. Is this a type one error or Type two error? 4 Math 260 Quiz 2 Name: ____________________ ===================================================================================== Problem 5 A cigarette manufacturer wishes to test the claim that the variance of the nicotine content of its cigarettes is 0.34. Nicotine content is measured in milligrams, and assume that it is normally distributed. A sample of 26 cigarettes has a standard deviation of 1.16 milligram. At α=0.05, is there enough evidence to reject the manufacturer’s claim? a. What is the parameter of interest? b. State the null Hypothesis. c. State the alternative hypothesis. 5 Math 260 Quiz 2 Name: ____________________ ===================================================================================== d. Is this a right-tailed test, Left-tailed, or a two-tailed test? e. Which statistical distribution applies for this problem? f. Find the critical values? Show the critical values on the graph of the distribution, and identify the rejection region and non-rejection region g. Compute the test values. h. Make your decision based the test vales and the critical values. i. Summarize the results. j. Is this a type one error or Type two error? 6 Math 260 Quiz 2 Name: ____________________ ===================================================================================== 7

Tutor Answer

Chem97
School: Boston College

Hi there :). I am back...here is your assignments :). Kindly open the attached files :)

Math 260

Quiz 2

Name: ____________________

Problem 1

Is there a difference in average miles traveled for each of two taxi companies
during a randomly selected week? The data are:
Yellow Cab Company
American United Company
X1=837
X2=753
σ =30
σ =40
n1=35
n2=40
Use α= 0.05. assume that the populations are normally distributed.
a. State the null Hypothesis.
Answer: 𝐻0 : 𝜇1 − 𝜇2 = 0
b. State the alternative hypothesis.
Answer: 𝐻1 : 𝜇1 − 𝜇2 ≠ 0
c. Is this a right-tailed test, Left-tailed, or a two-tailed test?
Answer: The hypothesis given would be two-tailed test.
d. Which statistical distribution applies for this problem?
Answer:
Decision rule: Reject H0 if test statistic value greater than critical value
e. Find the critical values? Show the critical values on the graph of the distribution, and
identify the rejection region and non-rejection region
Answer:
From the standard normal table, at 5% level of significance, the critical value would be
1.96 and below is the graph:

f. Compute the test values.
Answer:

1

Math 260

Quiz 2

𝑍0 =

Name: ____________________

̅̅̅1 − 𝑋
̅̅̅2 ) − (𝜇1 − 𝜇2 )
(𝑋
𝜎 2

√( 𝑛1 +
1

=

𝜎2 2
𝑛2

)

(837 − 753) − 0
302



35

+

402
40

84
=
8.1064
= 𝟏𝟎. 𝟑𝟔
g. Make your decision based the test vales and the critical values.
Answer:
The test statistic value is greater than the critical value (1.96). Hence, we reject the null
hypothesis at 5% level of significance.
h. Summarize the results.
Answer:
There is sufficient evidence that there is a difference in a an average miles traveled for
each two taxi companies during a randomly selected week.
Problem 2
Two brands of batteries are tested, and their voltages are compared. The summary
statistics follow. Find the 95% confidence interval of the true difference in the means. Assume
that both variables are normally distributed.
Exercise: Battery Voltage
Brand X
Brand Y

Answer:
̅ = 9.2 − 8.8 = 0.4
𝐷
0. 32 0. 12
0.4 + (1.96)√
+
< 𝜇1 − 𝜇2 <
27
30
0. 32 0. 12

0.4 + (1.96)
+
27
30

2

Math 260

Quiz 2

Name: ____________________

0.281 < 𝜇1 − 𝜇2 < 0.519
OR, 0.3 < 𝜇1 − 𝜇2 < 0.5

Problem 3 The number of murders and robberies per 100,000 population for a random
selection of states is shown. Is there a linear relationship between the variables?
Murders 2.4 2.7 5.6 2.6 2.13.3 6.6 5.7
Robberies 25.314.3151.691.1 80 49 17395.8
a. Draw the scatter plot for the variables.
Answer:

b. Compute the value of the correlation coefficient.
Answer:
Correlation coefficient=CORREL(x,y)=0.8043

c. State the hypotheses.
Answer:

d. Test the significance of the correlation coefficient at α = 0.05, using Table I.
3

Math 260

Quiz 2

Name: ____________________

Answer:
We notice that the sample size is 8, so, the we get ...

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Review

Anonymous
Tutor went the extra mile to help me with this essay. Citations were a bit shaky but I appreciated how well he handled APA styles and how ok he was to change them even though I didnt specify. Got a B+ which is believable and acceptable.

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