Question

A manufacturer produces ball bearings, normally distributed, with unknown mean and standard deviation. A sample of 25 has a mean of 2.5cm. The 99% confidence interval has length 4cm (double-sided).

1. Which statement is correct (use t-distribution):

1. s² = 23.42cm²        b) s² = 12.82cm²              c)   s= 3.58cm                   d) s= 4.84cm     

2. The 99% prediction interval measures (use t-distribution):

a) 20.38 cm                  b) 10.21 cm                      c) 20.42 cm                               d) 10.19 cm

From a box containing oatmeal bags, we get a sample of 10 bags. The weights are reported below. Assume that we know that the weight distribution follows a normal distribution, and that the standard deviation of the population of weight is s = 1.66.

Weights of the sample in oz:

3.       25.9    25.9     26.7     24.8     25.3     27.4     25.7     26.3     27.2

3. The 95% confidence interval for the mean of the population is:

a) C.I.= 26.15±1.03 oz   b) C.I.=26.15±1.03 oz²    c)   C.I.=26.15±0.31 oz d) C.I. = 26.15 oz

4. The 95% prediction interval for another oatmeal bag from the same brand is:

a) C.I.=26.15±1.03 oz   b) C.I.=26.15 oz²    c)   C.I.=26.15±3.41 oz       d)C.I.=26.15±1.03 oz²

5. The minimum sample size of oatmeal bags in order to be 95% confident that the estimate of m has an error less than 0.2 oz is:

a) 5                   b) 25                    c)   125                   d) 265

A company claims to have produced a new salad dressing contains an average of 100mg/l of trans-fat with a standard deviation of 2mg/l. Test Ho: m=100 versus H1: m≠100 with a sample of 16 specimens. Assuming distributions to be normal:

6. The error type I probability, if the acceptance region for the null hypothesis is 98.5 ≤ x ≤ 101.5, is :

a) 0.0013          b) 0.0026                         c)   0.0039              d) 0.0052

Answer 1