Question

a. Suppose that we want to show that the true mean weight of a lollipop is less than 1.5 ounces. Set up you null and alternative hypotheses to test this.

b. Suppose that the standard deviation is σ= 1 and the sample size is n= 100. If we observe a sample mean weight of Oreo cookies of 1.45 ounces, in words what is the p-value (referring to question 1)?

c­. How can you restate your answer for question 3?

Answer 1

Solution:

Part a

Here, we have to use one sample z test for the population mean, because we are given the value for the population standard deviation and sample size (n > 3) is adequate to use the one sample z test.

The null and alternative hypotheses are given as below:

Null hypothesis: H0: The true mean weight of a lollipop is 1.5 ounces.

Alternative hypothesis: Ha: The true mean weight of a lollipop is less than 1.5 ounces.

H0: µ = 1.5 versus Ha: µ < 1.5

This is a lower tailed (left tailed) test.

Part b

The test statistic formula is given as below:

Z = (Xbar - µ)/[σ/sqrt(n)]

From given data, we have

µ = 1.5

Xbar = 1.45

σ = 1

n = 100

We assume default level of significance α = 0.05

Critical value = -1.6449

(by using z-table or excel)

Z = (1.45 – 1.5)/[1/sqrt(100)]

Z = -0.5000

P-value = 0.3085

(by using Z-table)

Part c

For the above test, we have

P-value > α = 0.05

So, we do not reject the null hypothesis

There is not sufficient evidence to conclude that the true mean weight of a lollipop is less than 1.5 ounces.