Question

A recent national survey found that high school students watched an average (mean) of 7.1 movies per month with a population standard deviation of 1.0. The distribution of number of movies watched per month follows the normal distribution. A random sample of 41 college students revealed that the mean number of movies watched last month was 6.6. At the 0.05 significance level, can we conclude that college students watch fewer movies a month than high school students?

1. State the null hypothesis and the alternate hypothesis.

• H₀: μ ≥ 7.1; H₁: μ < 7.1

• H₀: μ = 7.1; H₁: μ ≠ 7.1

• H₀: μ > 7.1; H₁: μ = 7.1

• H₀: μ ≤ 7.1; H₁: μ > 7.1

2. State the decision rule.

• Reject H₁ if z < –1.645

• Reject H₀ if z > –1.645

• Reject H₁ if z > –1.645

• Reject H₀ if z < –1.645

3. Compute the value of the test statistic. (Negative amount should be indicated by a minus sign. Round your answer to 2 decimal places.)

4. What is your decision regarding H₀?

• Reject H₀

• Do not reject  H₀

5. What is the p-value? (Round your answer to 4 decimal places.)

Answer 1

Solutions Given that, x = 6.6 6 = 1.0 n= hl u= 7ol x= 0.05 The null and alternative hypothesis Hoolu Hae Fol 7. < This is left-tailed test a= 0005 Za= 2o.o5 = -10645 Z <-1.645 The critical value =-1645 Reject Ho if Z <-1.645 Test statistic, 2 = x-y 6 (In z = 6.6- 701 1.0/ 141

Solutions Given that, x = 6.6 6 = 1.0 n= hl u= 7ol x= 0.05 The null and alternative hypothesis Hoolu Hae Fol 7. < This is left-tailed test a= 0005 Za= 2o.o5 = -10645 Z <-1.645 The critical value =-1645 Reject Ho if Z <-1.645 Test statistic, 2 = x-y 6 (In z = 6.6- 701 1.0/ 141

Z The = -3.20 test statistic 2=-3.20 - 3.20 Test statistic < -10645 a critical value I Reject Ho. p-value = 0.0007