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# Analysis of variance

An article in the Wall Street Journal compares the performance of the largest Janus fund with the performance of the S&P 500. The comparison is achieved by assuming that\$10,000 was invested both in the Janus fund and in the S&P 500. Several months after the investments are made, a random sample of daily portfolio values are drawn from the very large chart presented in the article, and they lead to the following statistics. Sample sizes are 35 for each of the two hypothetical investments. For the Janus fund the sample average earnings is \$3,200 and the sample standard deviation is \$900; for the S&P 500, the average is \$2,800 and the standard deviation is \$800. Conduct a test of equality of performance of the two investments, using the 5% level of significance.

Suppose the USGA wants to compare the mean distances associated with four different brands of golf balls when struck with a driver. A completely randomized design is employed, with Iron Byron, the USGA's robotic golfer, using a driver to hit a random sample of 10 balls of each brand in a random sequence. The distance is recorded for each hit, and the results are shown below, organized by brand.

Golf Ball Test

(see chart in attached file)

Carry out a complete analysis using ANOVA and a 5% significance level.

#### Solution Summary

To test equality of performance of the two investments, using the 5% level of significance.

\$2.19