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# Mutual funds Investors Examined

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1. Periodically, Merrill Lynch customers are asked to evaluate Merrill Lynch financial consultants and services (2000 Merrill Lynch Client Satisfaction Survey). Higher ratings on the client satisfaction survey indicate better services, with 7 the maximum service rating. Independent samples of service ratings for two financial consultants are summarized here. Consultant A has 10 years of experience, whereas consultant B has 1 year of experience. Useα = 0.05 and test to see whether the consultant with more experience has the higher population mean service rating.
Consultant A Consultant B
n1 = 16 n2 = 10
x1 = 6.82 x2 = 6.25
s1 = 0.64 s2= 0.75

a. State the null and alternative hypothesis.
b. Compute the value of the test statistic
c. What is the p-value?

2. The grades of a sample of 5 students, selected from a large population, are given below.

70
80
60
90
75

a. Determine a point estimate for the variance of the population.
b. Determine a 95% confidence interval for the variance of the population.
c. At 90% confidence, test to determine if the variance of the population is
significantly more than 50.

3. Each day the major stock markets have a group of leading gainers in price (stocks that go up the most). On one day the standard deviation in the percent change for a sample of 10 NASDAQ leading gainers was 15.8. On the same day, the standard deviation in the percent change for a sample of 10 NYSE leading gainers was 7.9 (USA Today, September 14, 2000). Conduct a test for equal population variances to see whether it can be concluded that there is a difference in the volatility of the leading gainers on the two exchanges. Useα = 0.10. What is your conclusion?

4. The owner of a car wash wants to see if the arrival rate of cars follows a Poisson distribution. In order to test the assumption of a Poisson distribution, a random sample of 150 ten-minute intervals was taken. You are given the following observed frequencies:
Number of Cars Arriving
in a 10-Minute Interval Frequency
0 3
1 10
2 15
3 23
4 30
5 24
6 20
7 13
8 8
9 4

Useα = 0.10 to test if the above data have a Poisson distribution.

5. 7% of mutual fund investor rate corporate stocks "very safe", 58% rate them "somewhat safe", 24% rate them "not very safe", 4% rate them "not at all safe", and 7% are "not sure". A Business week/Harris poll asked 529 mutual fund investors how they would rate corporate bonds on safety. The responses are as follows.
Safety Rating Frequency
Very safe 48
Somewhat safe 323
Not very safe 79
Not at all safe 16
Not sure 63

Do mutual fund investor's attitudes towards corporate bonds differ from their attitudes toward corporate stocks? Support your conclusion with a statistical test. Use α = 0.01.