Many Mutual Funds Compare Their Performance With That Of A B

Many Mutual Funds Compare Their Performance With That Of a Benchmark

Many mutual funds compare their performance with that of a benchmark, an index of the returns on all securities of the kind that the fund buys. The Vanguard International Growth Fund, for example, takes as its benchmark the Morgan Stanley Europe, Australasia, Far East (EAFE) index of overseas stock market performance. Here are the percent returns for the funds and for the EAFE from 1982 (the first full year of the fund’s existence) to 2000: Year Fund EAFE Year Fund EAFE ......................................5 Make a scatterplot suitable for predicting fund returns from EAFE returns. Is there a clear straight-line pattern? How strong is this pattern? (Give a numerical measure.) Are there any extreme outliers from the straight-line pattern?

Which of the following values is not typically used for ? A.0.50 B.0.05 C.0.10 D.0.01 Question 2 of .0 Points In an article appearing in Today’s Health a writer states that the average number of calories in a serving of popcorn is 75. To determine if the average number of calories in a serving of popcorn is different from 75, a nutritionist selected a random sample of 20 servings of popcorn and computed the sample mean number of calories per serving to be 78 with a sample standard deviation of 7. Compute the z or t value of the sample test statistic. A.z = 1.916 B.t = -1.916 C.z = 1.645 D.t = 1.916 Question 3 of .0 Points A type I error occurs when the: A.sample mean differs from the population mean B.test is biased C.null hypothesis is incorrectly rejected when it is true D.null hypothesis is incorrectly accepted when it is false Question 4 of .0 Points The “Pizza Hot†manager commits a Type I error if he/she is A.staying with old style when new style is no better than old style B.switching to new style when it is no better than old style C.switching to new style when it is better than old style D.staying with old style when new style is better Question 5 of .0 Points A type II error occurs when: A.the sample mean differs from the population mean B.the null hypothesis is incorrectly rejected when it is true C.the null hypothesis is incorrectly accepted when it is false D.the test is biased Question 6 of .0 Points You conduct a hypothesis test and you observe values for the sample mean and sample standard deviation when n = 25 that do not lead to the rejection of H0. You calculate a p-value of 0.0667. What will happen to the p-value if you observe the same sample mean and standard deviation for a sample size larger than 25? A.The p – value may increase or decrease B.The p – value stays the same C.The p – value decreases D.The p – value increases Question 7 of .0 Points Suppose that the mean time for a certain car to go from 0 to 60 miles per hour was 7.7 seconds. Suppose that you want to test the claim that the average time to accelerate from 0 to 60 miles per hour is longer than 7.7 seconds. What would you use for the alternative hypothesis? A.H1: 7.7 seconds Question 8 of .0 Points Results from previous studies showed 79% of all high school seniors from a certain city plan to attend college after graduation. A random sample of 200 high school seniors from this city reveals that 162 plan to attend college. Does this indicate that the percentage has increased from that of previous studies? Test at the 5% level of significance. What is your conclusion? A.More seniors are going to college B.Reject H0. There is enough evidence to support the claim that the proportion of students planning to go to college is now greater than .79. C.Cannot determine D.Do not reject H0. There is not enough evidence to support the claim that the proportion of students planning to go to college is greater than .79. Question 9 of .0 Points A lab technician is tested for her consistency by taking multiple measurements of cholesterol levels from the same blood sample. The target accuracy is a variance in measurements of 1.2 or less. If the lab technician takes 16 measurements and the variance of the measurements in the sample is 2.2, does this provide enough evidence to reject the claim that the lab technician’s accuracy is within the target accuracy? State the null and alternative hypotheses. A.H0: ï³ï€²â‰¤ 1.2, H1: ï³ï€²> 1.2 B.H0: ï³ï€² ≥ 1.2, H1: ï³ï€² ≠1.2 C.H0: ï³ï€²

Paper For Above instruction

Mutual fund performance comparison is an essential aspect of investment analysis, providing stakeholders with benchmarks to evaluate the success of their investments. Many mutual funds compare their returns to relevant market indices, known as benchmarks, to gauge their relative performance. This practice allows investors to understand whether the fund manager is adding value beyond merely tracking the market's movements. For instance, the Vanguard International Growth Fund uses the Morgan Stanley Europe, Australasia, Far East (EAFE) index as its benchmark to measure overseas stock performance. Analyzing the fund's and the benchmark's returns over a specified period reveals how well the fund performs against market standards.

To evaluate the relationship between fund returns and benchmark indices, a scatterplot can be a useful initial tool. Plotting fund returns against EAFE returns from 1982 to 2000 enables visualization of their correlation, illustrating whether a linear pattern exists. If a clear straight-line pattern emerges, it indicates a strong linear relationship—suggesting predictability of fund returns based on benchmark performance. Quantitatively, this relationship can be measured using the correlation coefficient (r), which ranges from -1 to 1. An r value close to 1 indicates a very strong positive linear relationship, whereas an r near 0 suggests no linear correlation. The coefficient of determination (r²) further quantifies the percentage of variance in fund returns explained by the EAFE index. For instance, an r value of 0.85 would imply an r² of approximately 0.72, meaning about 72% of the variability in fund returns can be predicted from the benchmark data.

By examining the scatterplot and calculating correlation measures, we can identify potential outliers—data points that deviate significantly from the linear pattern. Outliers might distort the analysis, indicating unusual market periods, fund management issues, or data measurement errors. Identifying these points is crucial for robust statistical modeling and accurate prediction. If outliers are present, further analysis can determine if they should be excluded or if they reveal important insights about market conditions or fund behavior.

One critical aspect of statistical inference involves selecting an appropriate significance level, denoted typically by α. Typical values for α include 0.05, 0.10, and 0.01, corresponding respectively to 5%, 10%, and 1% levels of significance. In hypothesis testing, the p-value represents the probability of observing data as extreme as, or more extreme than, the actual observed data under the null hypothesis. A common threshold of α = 0.05 is used: if the p-value is less than this, the null hypothesis is rejected, indicating statistically significant evidence against it. Commonly, the value 0.05 is used for α because it balances the risks of Type I and Type II errors.

Beyond performance analysis, statistical tests are extensively used in health sciences, manufacturing, and social sciences to assess claims and hypotheses. For example, a nutritionist may test whether the average calorie content of popcorn differs from 75 calories using a t-test or z-test, depending on sample size and variance knowledge. Similarly, hypothesis tests evaluate claims about population means, proportions, variances, and other parameters, ensuring decisions are based on sound statistical principles rather than mere intuition.

In hypothesis testing, the risk of errors is a key consideration. A Type I error occurs when the null hypothesis is wrongly rejected when it is true, leading to a false positive conclusion. Conversely, a Type II error happens when the null hypothesis is falsely accepted when it is false, resulting in a missed detection of an actual effect. The significance level α directly influences the probability of making a Type I error—a smaller α reduces this chance but increases the risk of a Type II error. In medical testing, this balance is vital: overly strict significance reduces false positives but may miss genuine effects.

Sample size also impacts hypothesis testing outcomes and p-values. With larger samples, the estimates tend to be more precise, often leading to smaller p-values if an effect exists. For example, increasing the sample size from 25 to a larger number tends to decrease the p-value when the mean difference remains consistent, strengthening evidence against the null hypothesis. Conversely, if the same data show a p-value of 0.0667 at n=25, the p-value generally decreases as n increases, reflecting increased power of the test.

When formulating hypotheses about population means, the alternative hypothesis specifies the direction of the suspected effect. A one-sided (or one-tailed) alternative hypothesis states that the parameter is either greater than or less than the null value, not both. For example, testing whether the average acceleration time exceeds 7.7 seconds involves the alternative H₁: µ > 7.7 seconds. This approach allows focused testing; if data suggest the mean is longer, the null hypothesis can be rejected accordingly.

In public health and social sciences, proportion tests determine whether observed changes are statistically significant. For instance, testing whether the proportion of high school seniors planning to attend college has increased from a previous 79% involves hypothesis testing for proportions. Using sample data, the p-value indicates whether the observed increase is statistically significant at a given significance level (e.g., 5%). If the p-value is less than 0.05, the evidence supports a genuine increase in college attendance plans.

In quality control, tests on variances help monitor manufacturing consistency. For example, a technician's measurement variance is tested against a target variance using chi-square-based tests. If the sampled variance significantly exceeds the target, it suggests measurement inconsistency, prompting further investigation. Calculating the appropriate test statistic requires data such as sample size, variance, and degrees of freedom, which are then compared to critical values to determine statistical significance.

Furthermore, the precision of hypothesis tests depends on selecting correct critical values based on the significance level, sample size, and test distribution. For example, in testing the mean cost of books with a known standard deviation, critical z-values at the 0.05 significance level are approximately ±1.96. These values define the rejection regions for the null hypothesis in a two-tailed test.

Ultimately, understanding p-values and critical values allows researchers and decision-makers to draw valid conclusions about population parameters. A small p-value signals strong evidence against the null hypothesis, favoring alternative explanations. Conversely, a large p-value suggests insufficient evidence to reject the null. This framework is fundamental across disciplines, enabling data-driven decisions that stand up to statistical scrutiny.

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