Question

You love french fries and suspect that the serving sizes in the cafeteria vary too much. Some portions are too large while others are too small. The cafeteria claims that a serving of fries is 12 ounces. You and three of friends decide to test the cafeteria's claim. Each of you takes a sample by weighing the french fry servings in the cafeteria when each of you goes to each lunch this week.

1. State the hypothesis and create a hypothesis test for each sample at the 0.01 level of significance. Provide the test statistics and p-value for each test.

2. Compute the limits for the sample mean x-bar around mu = 12 such that, as long as a new sample mean is within those limits, the french fry weights will be considered acceptable.

Monday Lunch	Tuesday Lunch	Wednesday Lunch	Thursday Lunch
11.55	11.62	11.91	12.02
11.62	11.69	11.36	12.02
11.52	11.59	11.75	12.05
11.75	11.82	11.95	12.18
11.9	11.97	12.14	12.11
11.64	11.71	11.72	12.07
11.8	11.87	11.61	12.05
12.03	12.1	11.85	11.64
11.94	12.01	12.16	12.39
11.92	11.99	11.91	11.65
12.13	12.2	12.12	12.11
12.09	12.16	11.61	11.9
11.93	12	12.21	12.22
12.21	12.28	11.56	11.88
12.32	12.39	11.95	12.03
11.93	12	12.01	12.35
11.85	11.92	12.06	12.09
11.76	11.83	11.76	11.77
12.16	12.23	11.82	12.2
11.77	11.84	12.12	11.79
12	12.07	11.6	12.3
12.04	12.11	11.95	12.27
11.98	12.05	11.96	12.29
12.3	12.37	12.22	12.47
12.18	12.25	11.75	12.03
11.97	12.04	11.96	12.17
12.17	12.24	11.95	11.94
11.85	11.92	11.89	11.97
12.3	12.37	11.88	12.23
12.15	12.22	11.93	12.25

Answer 1

(1.) The hypothesis to be tested is:

H₀:The mean quantity of the fries served at the cafeteria is 12 ounces that is

Against the alternative hypothesis:

H₁:The mean quantity of the fries served at the cafeteria is not 12 ounces that is

The level of sgnificance in the study is 0.01.

The test statstc to be used is a Z statistics given as

The data can be analyzied using Excel to get the summary stats as follows:

So the Z-statistics is as follows

For Monday Lunch:

The p-value is:

For Tuesday Lunch:

The p-value is:

For Wednesday Lunch:

The p-value is:

For Thursday Lunch:

The p-value is:

(2.) For Monday Lunch the confidence interval is given as:

For Tuesday Lunch the confidence interval is given as:

​

For Wednesday Lunch the confidence interval is given as:

​

For Thursday Lunch the confidence interval is given as:

​

Thus as long as a new sample mean is within these limits, the french fry weights will be considered acceptable