Question

Adults around the world watch on average 4 hours of TV a day. A researcher thinks that Americans watch less TV than the international average. He finds 25 Americans who watch 3 hours of television a day on average, with a standard deviation of 2 hours. Using an Alpha = .05, test this hypothesis.

BE SURE TO ANSWER ALL PARTS OF THE QUESTION AND SHOW YOUR WORK WHEN YOU CAN.

a) What is the appropriate test?

b) State the null Hypothesis (in words and with means).

c) State the alternative hypothesis (in words and with means).

d) Find the critical value.

e) Calculate the obtained statistic.

f) Report the results. Make a decision

Answer 1

a) This is a One-Sample t-test.

Because the sample size is small (n =25 is less than 30) a t-distribution and as this is Left tailed test. So this is one sample t-test.

b) Null Hypothesis H0: The researcher thinks that Americans watch equal to 4 hours of TV than the international average i.e µ1 =4

c) Alternate Hypothesis Ha: The researcher thinks that Americans watch less than 4 hours of TV than the international average i.e µ1 <4. (Claim)

d)

Degree of freedom=n-1=25-1=24

alpha=0.05

Critical Value=-1.7109

e)The test statistic, t = (x - µ)/σ/√n =(3-4)/(2/√25)=-2.50

f)

The P value=0.0098

The critical value is -1.71.

Since -1.71 < -2.50, we can reject the null hypothesis.

There is sufficient evidence to conclude that the researcher thinks that Americans watch less than 4 hours of TV than the international average at 5% level of significance.

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