An investment analyst is evaluating the 10-year mean return on investment for industry-specific exchange-traded funds (ETFs) for three sectors: financial, energy, and technology. The analyst obtains a random sample of 30 ETFs for each sector and calculates the 10-year return of each ETF. The analyst has provided you with this data set.

Using the sample data, perform one-way analysis of variance (ANOVA). Evaluate whether the average return of at least one of the industry-specific ETFs is significantly different. Use a 5% level of significance.

Address the following items:

1. Define the null and alternative hypothesis in mathematical terms and in words.
2. Report the level of significance.
3. Provide your conclusion and interpretation of the test. Should the null hypothesis be rejected? Why or why not?
4. Does a side-by-side boxplot of the 10-year returns of ETFs from the three sectors confirm your conclusion of the hypothesis test? Why or why not?

DATA BELOW:

financial energy technology 0 5.5 5.2 7.3 1 7.1 7.4 8.2 2 6.9 6.6 7.1 3 5.1 5.7 7.6 4 4.6 5.6 8.2 5 5.3 5.5 11.5 6 5.9 6.4 9.2 7 5.6 6.1 9.5 8 5.5 5.2 7.3 9 7.1 7.4 8.2 10 6.9 6.6 7.1 11 5.1 5.7 7.6 12 4.6 5.6 8.2 13 5.3 5.5 11.5 14 5.9 6.4 9.2 15 5.6 6.1 9.5 16 4.7 4.4 6.2 17 6.4 6.6 7.4 18 6.7 6.4 6.9 19 4.3 4.8 6.4 20 4.1 5.0 7.4 21 5.1 5.3 11.1 22 5.7 6.2 8.9 23 4.7 5.2 8.1 24 5.3 5.0 7.1 25 6.4 6.6 7.4 26 5.8 5.6 6.0 27 4.9 5.5 7.4 28 4.1 5.0 7.4 29 4.8 4.9 10.3