Question

A machine in the lodge at a ski resort dispenses a hot chocolate drink. The average cup of hot supposed to contain 7.75 ounces. Let’s assume that x has a normal distribution with a population standard deviation of 0.3 ounces. A random sample of 50 cups of hot chocolate from this machine had a mean content of 7.82 ounces. Do you think the machine needs an adjustment? Can we conclude at the 5% level of significance that the mean amount of hot chocolate is different than 7.75 ounces?

a) State the null hypothesis H and the alternate hypothesis H.

b) What is the value of the sample test statistic (either z or t)?

The sample test statistic is and the value is . .

c) Find the P-value or show the critical region and critical value(s) on a graph of the sampling

distribution.

The P-value is

d) Based on your answers for parts (a) through (c), will you reject or fail to reject the null

hypothesis? Explain your answer.

Answer 1

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Answer:

a)

Below are the null and alternative Hypothesis,
Null Hypothesis, H0: μ = 7.75
Alternative Hypothesis, Ha: μ < 7.75

b)

Test statistic,
z = (xbar - mu)/(sigma/sqrt(n))
z = (7.82 - 7.75)/(0.3/sqrt(50))
z = 1.65

c)

P-value Approach
P-value = 0.9505 ( from z table as it is left tailed)

For the graph draw critical region after 1.65 to the left as critical region

d)

As P-value > 0.05, we cannot reject the null hypothesis.