Part (a) According to the National Association of Insurance Commissioners, the mean expenditure for auto insurance in North Carolina was $705 in 2017. An insurance salesperson in NC believes that the mean expenditure for auto insurance is less today. He obtains a simple random sample of 36 auto insurance policies and determines the mean expenditure to be $681 with a standard deviation of $40. Is there enough evidence to support the salesperson's claim that the mean expenditure for auto insurance is less than the 2017 amount at the a= 0.05 level of significance? Answer Step O: Verify Assumptions Is the sample n obtained by simple random sampling (SRS)? Is the sample size n ≥ 30 ? Step 1: Null and alternative hypotheses Ho : μ = Is the sample size n no more than 5% of the population size N (i.e. n < 0.05 N)? Step 2: Test statistic to= Step 3: Classical and p-value approaches -ta= p-value = (yes, no) Step 4: Conclusion versus H₁ μ Does the test statistic fall (lie) in the rejection (critical) region? (Round the critical value to 2 decimal places) The confidence interval is ( (Round the p-value to 4 decimal places) (Reject, Fail to reject) Ho. There (yes, no) H₁. Part (b) Use part (a) to construct a 99% confidence interval about the population mean μ. (yes, no) (is, is not) sufficient evidence at the 0.05 significant level to support the alternative hypothesis (yes, no) ). (Round to 2 decimal places).
Part (a) According to the National Association of Insurance Commissioners, the mean expenditure for auto insurance in North Carolina was $705 in 2017. An insurance salesperson in NC believes that the mean expenditure for auto insurance is less today. He obtains a simple random sample of 36 auto insurance policies and determines the mean expenditure to be $681 with a standard deviation of $40. Is there enough evidence to support the salesperson's claim that the mean expenditure for auto insurance is less than the 2017 amount at the a= 0.05 level of significance? Answer Step O: Verify Assumptions Is the sample n obtained by simple random sampling (SRS)? Is the sample size n ≥ 30 ? Step 1: Null and alternative hypotheses Ho : μ = Is the sample size n no more than 5% of the population size N (i.e. n < 0.05 N)? Step 2: Test statistic to= Step 3: Classical and p-value approaches -ta= p-value = (yes, no) Step 4: Conclusion versus H₁ μ Does the test statistic fall (lie) in the rejection (critical) region? (Round the critical value to 2 decimal places) The confidence interval is ( (Round the p-value to 4 decimal places) (Reject, Fail to reject) Ho. There (yes, no) H₁. Part (b) Use part (a) to construct a 99% confidence interval about the population mean μ. (yes, no) (is, is not) sufficient evidence at the 0.05 significant level to support the alternative hypothesis (yes, no) ). (Round to 2 decimal places).
MATLAB: An Introduction with Applications
6th Edition
ISBN:9781119256830
Author:Amos Gilat
Publisher:Amos Gilat
Chapter1: Starting With Matlab
Section: Chapter Questions
Problem 1P
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Question

Transcribed Image Text:Part (a)
According to the National Association of Insurance Commissioners, the mean expenditure for auto insurance in North Carolina was $705 in 2017. An insurance
salesperson in NC believes that the mean expenditure for auto insurance is less today. He obtains a simple random sample of 36 auto insurance policies and determines
the mean expenditure to be $681 with a standard deviation of $40. Is there enough evidence to support the salesperson's claim that the mean expenditure for auto
insurance is less than the 2017 amount at the a = 0.05 level of significance?
Answer
Step 0: Verify Assumptions
Is the sample n obtained by simple random sampling (SRS)?
Is the sample size n > 30 ?
Is the sample size n no more than 5% of the population size N (i.e. n
Step 1: Null and alternative hypotheses
Ho : μ =
Step 2: Test statistic
to =
Step 3: Classical and p-value approaches
-ta=
p-value =
Step 4: Conclusion
(yes, no)
Does the test statistic fall (lie) in the rejection (critical) region?
H₁.
versus H1 : μ
(Round the critical value to 2 decimal places)
The confidence interval is (
(Round the p-value to 4 decimal places)
(Reject, Fail to reject) Ho. There
(yes, no)
0.05 N)?
Part (b)
Use part (a) to construct a 99% confidence interval about the population mean u.
(yes, no)
(is, is not) sufficient evidence at the 0.05 significant level to support the alternative hypothesis
(yes, no)
). (Round to 2 decimal places).
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Step 1: Write the given information.
VIEWStep 2: Verify assumptions for the given scenario.
VIEWStep 3: Determine the null and alternate hypothesis.
VIEWStep 4: Determine the test statistics and critical value.
VIEWStep 5: Determine the p-value and conclusion for the hypothesis test.
VIEWStep 6: Determine the 99% confidence interval for the population mean.
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