A cookie manufacturer claims that its new cookies have more fiber than the ones produced by its competitor. The table shows the fiber content in seven samples of each type of cookies produced by the manufacturer and his competitor. At \(\alpha=0.01\), is there enough evidence to support the cookie manufacturer's claim?

(a) identify the claim and state \(H_{0}\) and \(H_{a}\),

(b) find the critical value(s) and identify the rejection region(s),

(c) calculate \(\bar{d}\) and \(s_{d}\),

(d) find the standardized test statistic \(t\),

(e) decide whether to reject or fail to reject the null hypothesis, 

(f) interpret the decision in the context of the original claim. Assume the samples are random and dependent, and the populations are normally distributed.

Transcribed Image Text:

Sample Fiber in manufacturer's sample Fiber in competitor's sample 1 2 3 4 5 6 7 25 28 24 27 27 30 20 20 30 32 32 222 21 17 21 27 27 22 24 17 19