Homework 3

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Pennsylvania State University *

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Mathematics

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Jan 9, 2024

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docx

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MTH 1014 Homework 3 Due: October 31 2023 at 1:50pm All work must be shown 1. The following table shows the cross-classification of hedge funds by market capitalization (either small, mid, or large cap) and objective (either growth or value). Growth Value Large Cap 23 19 Mid Cap 9 10 Small Cap 17 72 Does the evidence suggest market capitalization and objective are dependent at the 5% significance level? 2. MARS claims that Skittles candies should be comprised of 30% purple, 10% orange, and 20% should be red, yellow, and green. Business students count a large bag of Skittles and find 265 red, 279 purple, 303 yellow, 271 green, and 212 orange candies. Does the evidence suggest that at least one proportion is different from the claimed value at the 5% significance level? 3. A manufacturer has test-marketed a new men s cologne. Simple random samples of male ʹ students at a university were asked to try the product for four weeks and then were asked the question: Would you purchase the product? The results are shown in the following ʺ ʺ table: Soph. Jr. Sr. Will not purchase 13 12 25 Will purchase 87 88 275 Would you conclude the respondents preferences are independent of year in college? Conduct ʹ the test at α = 0.05.
4. The manager of a commercial mortgage department of a large bank has collected data during the past two years concerning the number of commercial mortgages approved per week. The results from these two years (104 weeks) indicated the following: Does the distribution of commercial mortgages approved per week follow a Poisson distribution? (Use the 0.01 level of significance.) 5. The following table shows the observed frequencies of the quarterly returns for a sample of 60 hedge funds. The table also contains the hypothesized proportions of each class assuming the quarterly returns have a normal distribution. The sample mean and standard deviation are 3.6% and 7.4% respectively. Class Observed Return < −5 14 −5 ≤ Return < 0 11 0 ≤ Return < 5 10 5 ≤ Return < 10 11 Return ≥ 10 14 Does the evidence suggest that the quarterly returns do not have a normal distribution at the 10% significance level? Mortgages Approved Frequency 0 14 1 18 2 26 3 19 4 19 5 16
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