Question

47. A shampoo manufacturer claims that consumers are getting a mean volume equal to 32 oz. of shampoo per bottle. 36 bottles are randomly selected and their amounts are listed below. Use 0.10 significance level to test the claim that the manufacturer claims are correct (7 points). 32.09 31.89 31.06 32.03 31.42 31.39 31.75 31.53 32.42 31.56 31.95 32.00 31.39 32.09 31.67 31.47 32.45 32.14 31.86 32.09 32.34 32.00 30.95 33.53 32.17 31.81 31.78 32.64 31.06 32.64 32.20 32.11 31.42 32.09 33.00 32.06 90:

Answer 1

Given that n=36 a=0.10 Hypothetical mean = 32oz. For given sariple sample mean mean = En n X = 1152:05 32.001388 36 1.-320014 Sambile standard deviation Ss. LEX; -3)? $ - (32:09 -32.0014)? +(32.06 - 32.001412 .36-1 şi = 0.5309 n-l 132.09 Null hypothesis Homegn volume equal to 32 fan Hoi l = 32 Alternative thypothesis._.His mean valme does not equal to 32o2. gre. Hi u +32 We are using it - test t-test since population stand and deviation is unknown. test statistic ta X-M slun t3?:0014 - 32 10.0158 0.5309/436 t=0.0158 Critical t-value ata=0.10 and df=n-1= 36-1 =35 = 1.690

then Since calculated salic is less than erlitical value Fail to reject null hypothesis at ásojo. Therefore there is nost that m an Volume is not equal to 3.2. to support enough evidence ms