The number of entrees purchased in a single order at a Noodl

The number of entrees purchased in a single order at a Noodles & Company restaurant has had an historical average of 1.5 entrees per order. On a particular Saturday afternoon, a random sample of 42 Noodles orders had a mean number of entrees equal to 1.85 with a standard deviation equal to 0.73. At the 1 percent level of significance, does this sample show that the average number of entrees per order was greater than expected?

a) Calculate the t statistic (Round your answer to 2 decimal places.)

Solution

(a) The test statisitc is

t=(xbar-mu)/(s/vn)

=(1.85-1.5)/(0.73/sqrt(42))

=3.11

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(b) It is a right-tailed test.

The degree of freedom =n-1=42-1=41

So the p-value= P(t with df=41>3.11)=0.0017 (from standard normal table)