Question

The manufacturer of processed deli meats reports that the standard deviation of the number of carbohydrates in its smoked ham is 0.6 gram per 2-ounce serving. A dietician believes it is higher than this, so she randomly selects 48 of the 2-ounce servings of smoked ham and determines that the standard deviation of the number of carbohydrates is 0.72 gram per serving. Is there sufficient evidence to indicate that the standard deviation is higher than 0.6 gram per serving at the 0.05 level of significance? Assume that all the requirements for hypothesis testing are met. Answer questions 11-13 and round to three decimal places. 11. What are the null hypothesis H, and alternative hypothesis HA? a. Ho: 0 = 0.6, HA: 0 > 0.6 b. H.: 0 = 0.72, HA: 0 >0.72 C. Ho : 0 = 0.6, HA: 0 < 0.6 d. H.: 0 = 0.72, HA: 0< 0.72 12. Find the test statistic x’and the P-value in this order. a. 56.4 and 0.163 b. 40.608 and 0.731 C. 67.68 and 0.026 d. 47 and 0.044 13. State the conclusion. a. Do reject the Ho, there is sufficient evidence for Ha. b. Do reject the Ho, there is not sufficient evidence for Ha. c. Do not reject the Ho, there is sufficient evidence for Ha. d. Do not reject the He, there is not sufficient evidence for Ha.

Answer 1

lle Null hypothesis Ho and Ho and Alternative hypothesis HA a. Ho : 0.6 Hair > 0.6 12. Test statistic (X.2) = (-1) 52 where, n = 48 S= 0.72 to= 0.6 2 = 47 x 6.72) (0-6)? ... Test statistic (22) = 67.68 0.026 :p-value (source: STATKEY Cimage a attached) Sog answer is option C. 67-68 and 0.026 X 13. Rejection Criteria Reject Ho if p-value < Reject of .0.026 < 0.05 je, Ho if → condition satisfied So, answer- Do reject Hog a. there is sufficient sufficient evidence for HA.

StatKey Theoretical Distribution Chi-squared Distribution- Reset Plot Chi-squared Distribution 0.045 Left Tail Two-Tail Right Tail df 47 0.040 Edit Parameters 0.035 0.030 0.025 0.020 0.026 0.015 0.010 0.005 0.000 10 20 30 40 50 60 70 80 67.680 Activate Windows

The test statistic is calculated using the formula mentioned. The p value is obtained from STATKEY (image attached for reference). We compare the p value with alpha and make the required decision.