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Required information [The following information applies to the questions displayed below.] A recent national survey found that high...

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Statistics

Required information

[The following information applies to the questionsdisplayed below.]

A recent national survey found that high school students watchedan average (mean) of 6.7 DVDs per month with a population standarddeviation of 0.80 hour. The distribution of DVDs watched per monthfollows the normal distribution. A random sample of 40 collegestudents revealed that the mean number of DVDs watched last monthwas 6.20. At the 0.05 significance level, can we conclude thatcollege students watch fewer DVDs a month than high schoolstudents?

a.State the null hypothesis and the alternate hypothesis.

Multiple Choice

  • H0: μ ≤ 6.7 ; H1: μ >6.7

  • H0: μ = 6.7 ; H1: μ ≠6.7

  • H0: μ > 6.7 ; H1: μ =6.7

  • H0: μ ≥ 6.7 ; H1: μ <6.7

b.State the decision rule.

Multiple Choice

  • Reject H0 if z < -1.645

  • Reject H1 if z > -1.645

  • Reject H0 if z > -1.645

  • Reject H1 if z < -1.645

c.

Compute the value of the test statistic. (Negativeamount should be indicated by a minus sign. Roundyour answer to 2 decimal places.)

  Value of the test statistic  
d.What is your decision regarding H0?

Multiple Choice

  • Reject H0

  • Cannot reject H0

Answer & Explanation Solved by verified expert
4.0 Ratings (567 Votes)

a) H0: μ ≥ 6.7 ; H1: μ < 6.7

b) Reject H0 if z < -1.645

c) population std dev ,    σ =    0.8000                  
Sample Size ,   n =    40                  
Sample Mean,    x̅ =   6.2000                  
                          
'   '   '                  
                          
Standard Error , SE = σ/√n =   0.8000   / √    40   =   0.1265      
Z-test statistic= (x̅ - µ )/SE = (   6.200   -   6.7   ) /    0.1265   =   -3.95

d)

Reject Ho
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