The weights of soy patties sold by Veggie Burgers Delight ar

The weights of soy patties sold by Veggie Burgers Delight are normally distributed. A random sample of 18 patties yields a mean weight of 3.72 ounces with a sample standard deviation of 0.6 ounces. At the .05 level of significance, perform a hypothesis test to see if the true mean weight is less than 4 ounces. What is the standard error of the mean? What is the null hypothesis? Is the alternative one - or two-sided? What is the value of the test statistic? What is the P-value of the test statistic? What do you conclude at alpha = .05?

Solution

a)

standard error of mean = std/sqrt(n)

= 0.6/sqrt(18)

= 0.1414

b)

null hypothesis

Ho: u < 4

Ha: u >=4

c)

alternate hypothesis is one sided

d)

test statistic

= x-u/standard error

= 3.72 -4 /0.1414

= -1.98

e)

P -value =

P(Z > -1.98) = 0.9761

f)

at alpha =0.05 we conclude there is sfficient evidence to reject null hypothesis