Question

2.2.14 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.

The number 1.97 is a statistics because it is sample standard deviation. We assign the symbol s .

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

Answer)

A)

1.97 is statistics

As it is sample s.d

B)

Null hypothesis Ho : u = 2.75

Alternate hypothesis Ha : u not equal to 2.75

As the population s.d is unknown here we will use t.distribution to conduct the test

Test statistics t = (sample.mean - claimed mean)/(s.d/√n)

t = (3.01 - 2.75)/(1.97/√100) = 1.32

C)

Degrees of freedom is = n-1 = 99

For 99 dof and 1.32 test statistics

P-value.from.t.distribution is = 0.1899

As the p-value is extremely large

We fail.to reject.the.null hypothesis Ho

So, we do not.have enough evidence to.conclude that mean is different from 2.75