Write your answers on a separate sheet(s) of paper. When writing test hypotheses
ID: 3233340 • Letter: W
Question
Write your answers on a separate sheet(s) of paper. When writing test hypotheses, use both symbolic notation and English to explain what the hypotheses represent. Answer questions 1 through 7 using the following information: M&M; Milk Chocolate candies are packaged in single serving bags with a stated content net weights of 47.9 grams. A random sample of packaging of M&M;'s was taken and content weights determined. The data of net weights of the 30 sampled bags of M&M;'s are given in the following table. 1. Find the sample mean, sample variance and standard deviation, and 5-number summary (minimum, first quartile, median, third quartile and maximum) for the data set of net weights (these statistics are listed in table at right). 2. Between what weights would we expect to see 95% of the M&M; net content weights? 3. Write the null and alternative hypotheses for the test of hypotheses that will determine if the actual mean weight content of a bag of M&M; Milk Chocolate candies is at least 47.9 grams. (Remember both H_0 and H_A need to be stated.) 4. What would be the value of the appropriate test statistic for this hypothesis test? 5. What is the P-value of the test statistic determined in question #3? 6. What would be the decision for this hypothesis test? (reject or do not reject the null hypothesis?) 7. State your conclusion based on the selected decision in question #5, appropriate to the hypothesis test on mean weights of M&M; bags.Explanation / Answer
Q>2 Here mean of the sample xbar = 48.11
And standard deivation s = 1.112
so this question indirectly demands 95% confidence interval of population mean which is equal to
xbar +- t0.025, 29 (s/n)
= 48.11 +- 2.045 * (1.112/30)
= (47.695, 48.525)
Q.3
Null HYpothesis : H0 : Actual mean weight of M & M milk chocolate candies is less than 47.9 grams. < 47.9
ALternative Hypothesis : Ha : Actual Mean weight of M& M Milk chocolate candies is less than 47.9 grams. >= 47.9
4. Test statistic
t = (xbar - )/ (s/n) = ( 48.11 - 47.90)/ (1.112/30) = 0.21/ 0.203 = 1.0344
5. P - value = Pr(xbar >= 48.11 ; 47.90 ; 0.203) = 0.1549
calculated by t - table
Q.6 We can not reject the null hypothesis.
Q.7 On the basis of Part (5) , we can conclude that mean weight is no greater than 47.90 grams and it is equal or less than 47.90 grams.
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