Q1 In the past a company used to produce 40 tons of a certai

Q1)

In the past, a company used to produce 40 tons of a certain food per day on average.

Now, using a new technology, the mean daily yield of the food for a random sample of

25 days of production is 45 tons with a standard deviation of 5 tons. Assume that the

daily yield of this food is normally distributed. Company claims average food per day has increase now compared to the past.

A.) Set up null and alternative hypothesis for the test

B.) Identify the test, Calculate critical value under 5% significance level

C.) Calculate the test statistic

D.) Carry out the test, state your results.

A.
Ho: u <= 40
Ha u > 40

B. As n > 30, it will be a right tailed z test.

zcrit = 1.645

z = (Xbar - uo) * sqrt(n) / s

Then

z = 5.00

As z > zcrit, we reject the null hypothesis.

There is a significant evidence that the new production yield is greater than the past, which is just 40 tons.