Question

Reconsider Dr. Sameer's research question about how much time Cal Poly students spend on watching television. Suppose that for the random sample of 100 Cal Poly students the mean number of hours per day spent watching TV turns out to be 3.01 hours, and the standard deviation of the number of hours per day spent watching TV turns out to be 1.97 hours.

a. Is the number 1.97 a parameter or a statistic? Assign an appropriate symbol to this number.
b. Find the standardized statistic to investigate whether the data provide evidence that the average number of hours per day Cal Poly students spend watching TV is different from 2.75 hours.
c. What is your conclusion about the hypotheses, based on the calculated value of the standardized statistic? How are you deciding?

Answer 1

a. 1.97 is a statistic

b. t test is = 1.32

p value = 0.186

c. there is not enough evidence to support our claim

Explanation:

a. 1.97 is not a parameter it is a statistic. It is the standard deviation of the sample. we represent this with the symbol s.

b. we are claiming that the mean hours that are spent watching television is different from 2.75

we form our hypothesis as:

h0; u = 2.75

h1: u not equal to 2.7

t stat = barx - u/s/√n

= 3.01-2.75/(1.97/√100)

= 0.26/(1.97/10)

= 0.26/0.197

= 1.32

we get p value

n = 100

df = 100-1 = 99

using t distribution, pvalue = 0.1899

c. the p value is higher than our alpha level here

0.189 > 0.05, so we fail to reject H0. our conclusion is that there is not enough evidence to show that μ is different from 2.75