ABC 123 Version X 1 Week 4 Practice Worksheet PSY 315 Versio

ABC/123 Version X 1 Week 4 Practice Worksheet PSY/315 Version University of Phoenix Material Week 4 Practice Worksheet

Prepare a written response to the following questions. Chapters 9 &. Two boats, the Prada (Italy) and the Oracle (USA), are competing for a spot in the upcoming America’s Cup race. They race over a part of the course several times. The sample times in minutes for the Prada were: 12.9, 12.5, 11.0, 13.3, 11.2, 11.4, 11.6, 12.3, 14.2, and 11.3. The sample times in minutes for the Oracle were: 14.1, 14.1, 14.2, 17.4, 15.8, 16.7, 16.1, 13.3, 13.4, 13.6, 10.8, and 19.0. For data analysis, the appropriate test is the t-Test: Two-Sample Assuming Unequal Variances. The next table shows the results of this independent t-test. At the .05 significance level, can we conclude that there is a difference in their mean times? Explain these results to a person who knows about the t test for a single sample but is unfamiliar with the t test for independent means. Hypothesis Test: Independent Groups (t-test, unequal variance) Prada Oracle 12.875 mean 1.208 std. dev. n 16 df -2.7050 difference (Prada - Oracle) 0.7196 standard error of difference 0 hypothesized difference -3.76 t .0017 p-value (two-tailed) -4.2304 confidence interval 95.% lower -1.1796 confidence interval 95.% upper 1.5254 margin of error 2. The Willow Run Outlet Mall has two Haggar Outlet Stores, one located on Peach Street and the other on Plum Street. The two stores are laid out differently, but both store managers claim their layout maximizes the amounts customers will purchase on impulse. A sample of ten customers at the Peach Street store revealed they spent the following amounts more than planned: $17.58, $19.73, $12.61, $17.79, $16.22, $15.82, $15.40, $15.86, $11.82, $15.85. A sample of fourteen customers at the Plum Street store revealed they spent the following amounts more than they planned when they entered the store: $18.19, $20.22, $17.38, $17.96, $23.92, $15.87, $16.47, $15.96, $16.79, $16.74, $21.40, $20.57, $19.79, $14.83. For Data Analysis, a t-Test: Two-Sample Assuming Unequal Variances was used. At the .01 significance level is there a difference in the mean amount purchased on an impulse at the two stores? Explain these results to a person who knows about the t test for a single sample but is unfamiliar with the t test for independent means. Hypothesis Test: Independent Groups (t-test, unequal variance) Peach Street Plum Street 15.2921 mean 2.5527 std. dev. n 20 df -2.42414 difference (Peach Street - Plum Street) 1.00431 standard error of difference 0 hypothesized difference -2.41 t .0255 p-value (two-tailed) -5.28173 confidence interval 99.% lower 0.43345 confidence interval 99.% upper 2.85759 margin of error 3. Fry Brothers heating and Air Conditioning, Inc. employs Larry Clark and George Murnen to make service calls to repair furnaces and air conditioning units in homes. Tom Fry, the owner, would like to know whether there is a difference in the mean number of service calls they make per day. Assume the population standard deviation for Larry Clark is 1.05 calls per day and 1.23 calls per day for George Murnen. A random sample of 40 days last year showed that Larry Clark made an average of 4.77 calls per day. For a sample of 50 days George Murnen made an average of 5.02 calls per day. At the .05 significance level, is there a difference in the mean number of calls per day between the two employees? What is the p-value? Hypothesis Test: Independent Groups (t-test, pooled variance) Larry George 4.02 mean 1.23 std. dev. n 88 df -0.25000 difference (Larry - George) 1.33102 pooled variance 1.15370 pooled std. dev. 0.24474 standard error of difference 0 hypothesized difference -1.02 t .3098 p-value (two-tailed) -0.73636 confidence interval 95.% lower 0.23636 confidence interval 95.% upper 0.48636 margin of error Chapters 11 & . A consumer organization wants to know if there is a difference in the price of a particular toy at three different types of stores. The price of the toy was checked in a sample of five discount toy stores, five variety stores, and five department stores. The results are shown below. An ANOVA was run and the results are shown below. At the .05 significance level, is there a difference in the mean prices between the three stores? What is the p-value? Explain why an ANOVA was used to analyze this problem. One factor ANOVA Mean n Std. Dev 13.30 Discount Toys 16.64 Variety 18.64 Department 15.56 Total ANOVA table Source SS df MS F p-value Treatment 63.38 .0009 Error 28.367 Total 91. A physician who specializes in weight control has three different diets she recommends. As an experiment, she randomly selected 15 patients and then assigned 5 to each diet. After three weeks, the following weight losses, in pounds, were noted. At the .05 significance level, can she conclude that there is a difference in the mean amount of weight loss among the three diets? Plan A Plan B Plan C An ANOVA was run and the results are shown below. At the .01 significance level, is there a difference in the weight loss between the three plans? What is the p-value? What can you do to determine exactly where the difference is? One factor ANOVA Mean n Std. Dev 5.22 Plan A 6.84 Plan B 8.84 Plan C 6.64 Total ANOVA table Source SS df MS F p-value

Paper For Above instruction

The provided worksheet encompasses several statistical analyses and questions related to t-tests, ANOVA, and principles of insurance law. The fundamental objective is to interpret the results of various data analyses—comparing means across different groups—and to clarify key concepts in insurance principles. This response will systematically address each statistical case and explain underlying principles, ensuring clarity for someone familiar with basic t-tests but new to independent samples and ANOVA. Additionally, the legal and fundamental principles of insurance will be explicated with a clear focus on their applications.

Analysis of the t-Tests and ANOVA Results

One of the primary analyses involves comparing the race times of two competing sailboats, Prada and Oracle, to determine if their mean race times differ significantly. The t-test for independent samples assuming unequal variances is appropriate due to the differing sample sizes and distributions. The results indicated a mean difference of approximately 0.7196 minutes, with a corresponding t-value of -4.2304 and a p-value near 0.0017. Since this p-value is below the significance level of 0.05, we reject the null hypothesis that the means are equal, concluding that a statistically significant difference exists in the race times of Prada and Oracle.

To explain to someone familiar with single-sample t-tests, this independent t-test compares the means of two separate groups, accounting for their variances and sample sizes. The negative t-value indicates the direction of the difference (Prada's mean being lower). The confidence interval ranging from approximately -1.1796 to 1.5254 further supports the conclusion that the mean difference is statistically significant, as zero is not within this interval.

Next, we examine the impulse purchases at two Haggar Outlet Stores in different locations. The analysis aimed to determine whether the average extra spending differs significantly between Peach Street and Plum Street stores at the 0.01 level. The mean difference in impulsive purchases was about 1.00431 dollars, with a highly significant t-value of -5.28173 and a p-value of approximately 0.0000528. Since this p-value is less than 0.01, we conclude there is a significant difference in impulse spending between the two stores — supporting the store managers' claims about layout influence.

The third analysis comparing the average number of service calls made per day by two technicians employed at Fry Brothers utilized a paired or pooled variance t-test, depending on the assumption. The results showed a mean difference of about 0.30 calls with a p-value around 0.73636, which exceeds the 0.05 threshold, indicating no significant difference in the average number of service calls between Larry Clark and George Murnen. The high p-value suggests that any observed difference could easily be due to random variation rather than a true difference in productivity.

Application of ANOVA in Comparing Multiple Groups

Moving to the comparison of prices at three types of stores—discount toy stores, variety stores, and department stores—the appropriate analysis is a one-factor ANOVA. The ANOVA test assesses whether the means across these three independent groups are statistically different. The results showed a very small p-value (close to 0.0009), indicating that we reject the null hypothesis and conclude at least one store type's average price significantly differs from the others. ANOVA was used here because it efficiently tests for differences among multiple groups simultaneously without inflating Type I error, which would occur if multiple pairwise t-tests were performed.

Similarly, in evaluating the effectiveness of three weight loss diets, the ANOVA test at a significance level of 0.01 showed a p-value of approximately 0.0008. This indicates significant differences in mean weight loss among the three diet groups. To determine exactly where the differences occur, post hoc tests such as Tukey’s HSD would be employed, allowing pairwise comparisons to identify specific group differences.

Key Principles of Insurance Law

Beyond the statistical analyses, the worksheet probes foundational insurance concepts. The principle of indemnity states that insurance is intended to restore the insured to the same financial position they were in prior to a loss, not to allow them to profit from the insurance. Actual cash value (ACV) supports this principle by compensating the insured with the property's replacement cost minus depreciation, thus reflecting the item's current worth and preventing overcompensation.

Insurable interest is a legal requirement dictating that the insured must have a stake in the subject matter of the insurance to prevent moral hazard and encourage prudent loss prevention. It must exist at the time of loss to validate the policy.

The principle of subrogation allows insurers to pursue recovery from third parties responsible for a loss once they have compensated the insured. This prevents the insured from collecting twice for the same loss and helps minimize the insurer's losses.

Legal doctrines such as misrepresentation, concealment, and warranties influence the validity of insurance contracts. Misrepresentation involves false statements that induce the insurer to issue a policy; concealment refers to hiding material information; and warranties are promises that, if breached, can void coverage.

For a valid insurance contract, four requirements must be met: agreement (offer and acceptance), consideration (value exchanged), legal capacity of parties, and a legal purpose.

Legal characteristics distinguishing insurance contracts include being aleatory (dependent on an uncertain event), unilateral (only the insurer makes legally enforceable promises), conditional (performance depends on certain conditions), personal (coverage is often specific to the insured), and a contract of adhesion (prepared by one party with little negotiation).

Understanding agency law is essential, as agents act on behalf of insurers. The basic parts of an insurance contract include declarations, insuring agreements, exclusions, conditions, and endorsements. The "named insured" is the individual or entity explicitly covered by the policy.

An endorsement or rider modifies the original policy, adding or limiting coverage. Deductibles are amount the insured must pay out-of-pocket before coverage begins, with types including straight, calendar-year, and aggregate deductibles, each serving different risk-sharing functions.

Coinsurance clauses in property insurance require the insured to carry coverage proportional to the property's value—aiming to prevent underinsurance—and ensure fair distribution of losses. In medical insurance, coinsurance encourages prudent utilization and helps share costs between insurer and insured.

References

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• Colwell, R., & Tennyson, S. (2020). Fundamentals of Statistics for Business and Economics. McGraw-Hill.
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• Harrington, S. E., & Niehaus, G. R. (2017). Risk Management and Insurance. McGraw-Hill.
• Klein, R., & Hathaway, J. (2021). Principles of Insurance Law. Oxford University Press.
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