Question

A snack food manufacturer estimates that the variance of the number of grams of carbohydrates in servings of its tortilla chips is 1.11. A dietician is asked to test this claim and finds that a random sample o 22 ser ngs has a variance o 0.98 A α : 0.0 is there enough evidence o reject the man tacturers cam Assume the opulation is normally distributed complete parts (a) through (e) below (a) Write the claim mathematically and identify Ho and H OA. Ho02 s 1.11 (Claim) Ос. Hoơ2 # 1.11 ов, но : σ2 2 1.11 Ha σ2< 1.11 (Clam) Ha : σ2 1.11 D. Hoơ2-1.11 (Claim) ( Ha σ2: 1.11 (Claim) Ha : σ2t 1.11 (b) Find the critical value(s) and identify the rejection region(s) The critical value(s) is(are) Round to two decimal places as needed. Use a comma to separate answers as needed.) Choose the correct statement below and fill in the corresponding answer boxes A. The rejection regions are x2 . Ц and x3. O B. The rejection region is ° C. The rejection region isx, (c) Find the standardized test statistic x2 (Round to two decimal places as needed) (d) Decide whether to reject or fail to reject the null hypothesis, and (e) interpret the decision in the context of the original claim. Fill in the correct answers below Ho servings of its tortilla chips is 1.11 ' There enough evidence to a the 1% level o ificance to reject the manufacture scam that the var ance of um ber of grams o carbohydrates n s

Answer 1

H, : σ. 1.11 (Claim) H,:02#1.11 EXCEL (PH Stat) output:

Chi-Square Test of Variance Data Null Hypothesis Level of Significance Sample Size Sample Standard Deviation 1.11 0.01 0.98 Intermediate Calculations Degrees of Freedom Half Area Chi-Square Statistic 21 0.005 18.1697 Two-Tail Test Lower Critical Value 8.0337 41.4011 0.3618 Upper Critical Value Value Do not reject the null hypothesis The critical values are 8.03,41.40 A. The rejection regions are χ2 < 8.03 and > 41.40

The value of standardized test statistic is χ2-18.17 Do not relect Ho-There is not enough evidence to at the 1% level of significance to reject the manufacturer's cliam that the variance of the number of grams of carbohydrates in servings of its tortilla chips is 1.11