A recent national survey found that high school students watched an average (mea
ID: 2928227 • Letter: A
Question
A recent national survey found that high school students watched an average (mean) of 6.6 DVDs per month with a population standard deviation of 1.00 hour. The distribution of DVDs watched per month follows the normal distribution. A random sample of 30 college students revealed that the mean number of DVDs watched last month was 6.00. At the 0.05 significance level, can we conclude that college students watch fewer DVDs a month than high school students? 4. Required information a. State the null hypothesis and the alternate hypothesis. H0: > 6.6 ; H1: = 6.6 H0: = 6.6 ; H1: 6.6 H0: 6.6 ; H1: < 6.6 H0: 6.6 ; H1: > 6.6 b. State the decision rule. Reject H1 if z < -1.645 Reject H0 if z < -1.645 Reject H0 if z > -1.645 Reject H1 if z > -1.645 c. Compute the value of the test statistic. (Negative amount should be indicated by a minus sign. Round your answer to 2 decimal places.) Value of the test statistic d. What is your decision regarding H0? Cannot reject H0 Reject H0 e. What is the p-value? (Round your answer to 4 decimal places.)
Explanation / Answer
The statistical software output for this problem is:
One sample Z summary hypothesis test:
: Mean of population
H0 : = 6.6
HA : < 6.6
Standard deviation = 1
Hypothesis test results:
Hence,
a) Null and Alternative hypotheses:
H0: 6.6 ; H1: < 6.6
b) Reject H0 if z < -1.645
c) Test statistic = -3.29
d) Reject Ho
e) P - value = 0.0005
Mean n Sample Mean Std. Err. Z-Stat P-value 30 6 0.18257419 -3.2863353 0.0005