Answered: A sample of 14 cans of Brand A diet…

Glencoe Algebra 1, Student Edition, 9780079039897, 0079039898, 2018

18th Edition

ISBN:9780079039897

Author:Carter

Publisher:Carter

Chapter10: Statistics

Section10.3: Measures Of Spread

Problem 1GP

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A sample of 14 cans of Brand A diet cola gave the mean number of calories of 23 per can with a standard deviation of 3 calories. Another sample of 16 cans of Brand B diet cola gave the mean number of calories of 25 per can with a standard deviation of 4 calories. At the 1% significance level, can you conclude that the mean numbers of calories per can are different for these two brands of diet cola? Assume that the calories per can of diet cola are normally distributed for each of the two brands and that the standard deviations for the two populations are equal.

We are to test for the difference in the mean numbers of calories per can for the two brands. The null and alternative hypothesis are, respectively

The mean numbers of calories are not different

The mean numbers of calories are different

The critical values of t (for df_28 and .005 area in each tail of the t distribution curve) are -2.763 and 2.763. The value of the test statistics t = -1.531

Provide the following:

a. Decision (whether to accept or reject the null hypothesis)

b. Conclusion

Features Features Normal distribution is characterized by two parameters, mean (µ) and standard deviation (σ). When graphed, the mean represents the center of the bell curve and the graph is perfectly symmetric about the center. The mean, median, and mode are all equal for a normal distribution. The standard deviation measures the data's spread from the center. The higher the standard deviation, the more the data is spread out and the flatter the bell curve looks. Variance is another commonly used measure of the spread of the distribution and is equal to the square of the standard deviation.

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