# Independent sample t test for solar energy data

Solar Energy in Different Weather: A student of the author lives in a home with a solar electric system. At the same time each day, she collected voltage readings from a meter connected to the system and the results are listed in the accompanying table. Use a).05 significance level to test the claim that the mean voltage reading is the same for the three different types of day. Is there sufficient evidence to support a claim of different population means? We might expect that a solar system would provide more electrical energy on sunny days than on cloudy or rainy days. Can we conclude that sunny days result in greater amount of electrical energy? (See Excel data Solar Energy )

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Solar Energy in Different Weather: A student of the author lives in a home with a solar electric system. At the same time each day, she collected voltage readings from a meter connected to the system and the results are listed in the accompanying table. Use a).05 significance level to test the claim that the mean voltage reading is the same for the three different types of day. Is there sufficient evidence to support a claim of different population means? We might expect that a solar system would provide more electrical energy on sunny days than on cloudy or rainy days. Can we conclude that sunny days

result in greater amount of electrical energy? (See Excel data Solar Energy )

Sunny Days Cloudy Days Rainy Days

13.5

13.0

13.2

13.9

13.8

14.0

12.7

12.5

12.6

12.7

13.0

13.0 12.1

12.2

12.3

11.9

11.6

12.2

Ans.

Here the null hypothesis tested is Solar system will provide the same amount of energy in sunny days, Cloudy days and in Rainy days .

Rejection criteria: Reject the null hypothesis s if the calculated value of F is greater than the critical value of F

Anova: Single Factor

SUMMARY

Groups Count Sum Average Variance

Sunny Days 6 81.4 13.56666667 0.162667

Cloudy Days 6 76.5 12.75 0.043

Rainy Days 6 72.3 12.05 0.067

ANOVA

Source of Variation SS df MS F P-value F crit

Between Groups 6.914444 2 3.457222222 38.0379 1.33E-06 3.68232

Within Groups 1.363333 15 0.090888889

Total 8.277778 17

Conclusion

We reject the null hypothesis as the calculated value of F is greater than the critical value

It can be noted that sunny days average have an average of 13.566 and we can conclude that Can we conclude that sunny days result in greater amount of electrical ...

#### Solution Summary

The solution gives details of students t test for comparing the usage of solar energy. Null hypothesis, alternative hypothesis, critical value, P value and test statistic are given in the solution with interpretation.