A random sample of Oreo^TM chocolate sandwich cookies from the box on my desk ha

Question

A random sample of Oreo^TM chocolate sandwich cookies from the box on my desk has mean frosting mass 43 g with standard deviation 0.2 g. The manufacturer claims the mean frosting mass is 4.4 g. a. Construct a 98% confidence interval for the mean frosting mass in such cookies. b. Suppose the sample size was 10 cookies. What assumptions would you need to make before you could conduct a hypothesis test for whether the mean frosting mass is less than the manufacturer claims? c. Suppose the sample size was 35 cookies. Test the claim, at alpha = 0.01 (I'm very concerned about my cookies), that the mean frosting mass is less than the manufacturer claims. Report the test statistic, critical value, rejection result, and p-value.

Explanation / Answer

14 )

Xbar = 4. 3 , s = 0.2 , n

98 % confidence interval

(xbar - t * s/sqrt(n) , xbar + t * s/sqrt(n) )

(4.3 - t * 0.2/sqrt(n) , 4.3 + t* 0.2/sqrt(n))

t is t-critical for 98 % level of confidence with df = n-1

c) if n =35

TS = (Xbar - 4.4)/(s/sqrt(n))

=(4.3 - 4.4)/(0.2/sqrt(35))

=-2.9580398

df= n-1= 34

t-critical = -2.441

since |TS|>|t-critical|

we reject the null hypothesis

p-value = P(t < -2.9580398) = 0.0028

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