Question

1. According to a 2011 report by the U.S. Department of Labor, civilian Americans spend 2.75 hours per day watching television. A faculty researcher, Dr. Sameer, at California Polytechnic State University (Cal Poly) conducts a study to see whether a differentaverage applies to Cal Poly students. He surveys a random sample of 100 Cal Poly students and finds the mean number of hours spent watching TV is 3.07 hours. The sample standard deviation is 1 hours. The sample distribution is not strongly skewed.

1. Describe the parameter in words (1 pts). Assign a symbol to it. (0.5 pts)

2. What is the value for the statistic? (1 pts). Assign a symbol to it.(0.5 pts)

3. Describe the nullhypothesis in words. (2 pts)

4. Describe the alternativehypothesis in words. (2 pts)

5. Write your null hypothesis and alternative hypothesis from part c and d using symbols. (3 pts)

6. Why we can use theory-based approach for this study? (2 pts)

7. Calculate the t-statistic. Show your work. (4 pts)

8. Based on your t-statistic, do you have strong evidence against the null hypothesis? (1 pts)

1. Based on your result from part h, what type of error may occur? (1 pts)

10. Describe the type of error you identify in part I in the context of the question. (2 pts)

Answer 1

a) = 2.75

is the population mean time civilian Americans spend per day watching television.

b) = 3.07

is the sample mean time spend by the 100 Cal Poly students per day by watching television.

c) Null hypothesis: The population time spend by the civilian Americans in watching television per day is equal to 2.75 hours.      

d) Alternative hypothesis: The population time spend by the civilian Americans in watching television per day is not equal to 2.75 hours.

e) H₀: = 2.75

f) H₁: 2.75

g) The test statistic t = ()/(s/)

                                 = (3.07 - 2.75)/(1/)

                                 = 3.2

h) At 0.05 significance level, the critical values are +/- t_0.025 = +/- 1.984

Since the test statistic value is greater than the positive critical value(3.2 > 1.984), so we should reject the null hypothesis.

Yes, we have strong evidence against the null hypothesis.

i) The type I error may occur.

j) The Cal Poly students spend a different average time in watching television but in real the Cal Poly students spend equal average time in watching television as for the civilian Americans spend.