Question

3. A company claims that the new boxes of detergents that it sells contain more than 500 grams of detergent. From past experience the company knows that the quantity of t in a box is normally distributed with a mean of 500 grams and a standard deviation of 120 grams. A market analyst bought 64 boxes of the detergent and found that the average weight is 520 grams. Determine if the company's claim is legitimate at the 0.05 level of significance.

Answer 1

Test: μ > 500 with normal dist" Hypothesis test H0 : μ 500 Ha : μ > 500 Null Hypothesis, Ho 500 is also correct) (Alternative Hypothesis, also called H1) This is upper tailed test (one tailed test) 520 σ 120 n 64 Significance Level, a -0.05 Test statistic z Test Statistic. *520 500 Test Statistic, z' 1.33 1.3333331.33 120/v64 P-value is in direction of Alternative hypothesis Since Ha : μ > 500, P-value-P(Z > 1.33) P-value is Area to the right of test statistic 1.33 value 0.0918 test statistic 1.33 P-value P(Z 1.33) 0.0918 (from z-table)

Decision Rule (rejection criteria): Reject H0 if p-value < α Decision: Since 0.0918 0.05, we fail to reject the null hypothesis. Using excel function normdist-((520 - 500)/120/sqrt (64))),0,1, TRUE) or TI's function normaledf 1E-99, -( (520- 500)/( 120/sqrt(64))) answer is: 0.0912112197 The Critical Value-Zorit-za-z005-1645 (From z table , using interpola tion, 1/2 th distance between 1.64 and 1.65) Critical value 1.645 Decision Rule (rejection criteria): Reject Ho if z* tailed test) ze (because this is upper Rejection region has been shaded: a = 0.05 a 1.645 Decision: Since 0.0918 3 1.645, we fail t reject the mull hypothesis. Hence at 5% significance level, there is insufficient evidence to conclude that μ is greater than 500 Company's claim is NOT legitimate at 5% level of significance oaThank youe