Question

1. The data below represents the amount that a sample of fifteen customers spent for lunch ($) at a fast-food restaurant:

8.42   6.29   6.83   6.50   8.34   9.51   7.10   6.80   5.90   4.89   6.50   5.52   7.90   8.30   9.60

• At the 0.01 level of significance, is there evidence that the mean amount spent for lunch is different from $6.50? Follow and show the 7 steps for hypothesis testing.  
• Determine the p-value and interpret its meaning.
• What assumption must you make about the population distribution in order to conduct the test in part a? Is the assumption valid? Use and include an appropriate graph from Minitab. Write a couple of sentences supporting your answer.  
• Verify your results using Minitab by attaching or including the Minitab output.

2. Of 900 surveyed active LinkedIn members, 368 reported that they are planning to spend at least $1,000 on consumer electronics in the coming year.

• At the 0.05 level of significance, is there evidence that the percentage of all LinkedIn members who plan to spend at least $1,000 on consumer electronics is greater than 38%? Follow and show the 7 steps for hypothesis testing.
• Determine the p-value and interpret its meaning.
• What assumption must you make in order to conduct the test in part a? Demonstrate if the assumption is met.  
• Verify your results for parts a and b using Minitab. Attach or include your output.  

Answer 1

1. For the testing problem, population distribution is assumed to be normal.

Testing the validity of the assumption, using Minitab (Stat -> Basic Statistics -> Normality Test), we get the following output -

Since P-value = 0.584 > 0.05, so at 5% level of significance, we can conclude that population distribution is normal.

Let denotes the mean amount spent for lunch.

Verify the results using Minitab,