Assignment:
Q1. The manager of a driving school claims that the mean time taken to learn how to drive a car is 8 hours or less for all new drivers. A sample of 16 new drivers showed that the mean time taken by them to learn how to drive the car is 9.5 hours with a standard deviation of 1.5 hours. Test the manager's claim at the 1% significance level.
a. Select the null and alternate hypothesis.
1. Ho: µ = 8 H1: µ ≠ 8
2. Ho: µ = 9.5 H1: µ ≠9.5
3. Ho: µ = 8, H1: µ > 8
4. Ho: µ = 9.5, H1: µ > 9.5
b. Determine the critical values of the test statistic.
1. Reject if Z (obs) < Z (o.o1) = - 2.33
2. Reject if Z (obs) > Z (o.01) = 2.33
3 Reject if t (obs) < t (o.o1) = - 2.60
4. Reject if t (obs) > t (o.01) = 2.60
c. Which equation listed below would you use?
1. z = (x bar - µ) / s/vn
2. z = (p - p) / v p (1-p) / n
3. t= (x bar - µ) / s/vn
d. Using the statistical calculator or manual calculation what is the observed statistic and what is your decision regarding the null hypothesis. Provide a one sentence answer.
Q2. A department store manager claims that at least 45% of persons who visited this store make a purchase. In a sample of 400 persons who visited the store 150 made a purchase. Test the manager's claim at the 3% significance level.
a. State the null and alternate hypothesis.
1. Ho: p = 0.45, H1: p ? 0.45
2. Ho: p = 0.45, H1: p < 0.45
3. Ho: p > 0.45, H1: p = 0.45
4. Ho: p = 0.45, H1: p > 0.45
b. Determine the rejection region for the decision rule.
1. Reject if Z (obs) < Z (o.o3) = - 1.88
2. Reject if Z (obs) > Z (o.15) = 2.17
3 Reject if Z (obs) < Z (o.15) = - 2.17
4. Reject if Z (obs) > Z (o.03) = 1.88
c. Which equation listed below would you use?
1. z = (x bar - µ) / s/vn
2. z= (p - p) / v p (1-p) / n
3.t= (x bar - µ) / s/vn
d. Using the statistical calculator or manual calculation what is the observed statistic and what is your decision regarding the null hypothesis. Provide a one sentence answer.
Q3. Complete the ANOVA summary table shown here.
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Source of Variation
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Sum of Squares
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Degrees of freedom
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Mean Square
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F observed
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Between Treatments
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150.2
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9
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Error (Within Treatments)
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200.7
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Sums of Squares of Total
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39
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a. How many treatments are there?
b. What is the total sample size?
c. Is there a significant difference at the 5% Level of significance? Would I accept or reject the null Hypothesis. i.e. what is the critical value of the test statistic
d. Select one of the following.
1. There is a significant difference between the treatments
2. There is no significant difference between the treatments