The weights of soy patties sold by a diner are normally distributed. A random sample of 15 patties yields a mean weight of 3.8 ounces with a sample standard deviation of 0.5 ounces. At the 0.05 level of significance, perform a hypothesis test to see if the true mean weight is < 4 ounces. What is the correct conclusion at the 0.05 level of significance?

Question

Dylan Rivas

Mathematics

25 March, 22:43

The weights of soy patties sold by a diner are normally distributed. A random sample of 15 patties yields a mean weight of 3.8 ounces with a sample standard deviation of 0.5 ounces. At the 0.05 level of significance, perform a hypothesis test to see if the true mean weight is < 4 ounces. What is the correct conclusion at the 0.05 level of significance?

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Elliot Andrews · Answer 1

Step-by-step explanation:

Mean weigth is 3.8

standard deviation 15 = 0.5

sd2 = 15 * (sd₁₅) ²

sd = (15*0.25) ^0.5

sd=1.94

z = (3.8-4) / ((0.5) / 15^0.5)

z=-1.55

p=0.060571

0.060571>.05

true mean weight is less than 4 ounces

test statistic = (sample mean-mean) / ((sd of sample) / n^0.5)

test statistic = (3.8-4) / ((0.5) / 15^0.5)

test statistic=-1.55