Quiz
Quiz Review

1. From past records it is known that the average life of a battery used in a digital clock is 305 days.  The battery life is normally distributed.  The battery was recently modified to last longer.  A sample of 20 of the modified batteries was tested.  It was discovered that the mean life was 311 days and the sample standard deviation was 12 days.  We want to test at the 0.05 level of significance whether the modification increases the life of the battery.  What is our decision rule?
A: Do not reject the null hypothesis if computed t is 1.96 or greater
B: None of the above
C: Do not reject the null hypothesis if computed t is 1.729 or greater
D: Reject the null hypothesis if computed t is 2.086 or greater
2. A manufacturer wants to increase the absorption capacity of a sponge.  Based on past data, the average sponge could absorb 3.5 ounces. After the redesign, the absorption amounts of a sample of sponges were (in ounces): 4.1, 3.7, 3.3, 3.5, 3.8, 3.9, 3.6, 3.8, 4.0, and 3.9.  What is the decision rule at the 0.01 level of significance to test if the new design increased the absorption amount of the sponge?
A: Do not reject null hypothesis if computed t is less than 2.580
B: Do not reject null hypothesis if computed t is less than 2.821
C: Reject null hypothesis if computed z is 1.96 or larger
D: Reject null hypothesis if computed t is less than 2.764
3. If the alternate hypothesis states that m does not equal 4,000, what is the rejection region for the hypothesis test?
A: Both tails
B: Lower or left tail
C: Upper or right tail
D: Center
4. If the 1% level of significance is used and the computed value of z is +6.00, what is our decision?
A: Do not reject H0
B: Reject H0
C: Reject H1
D: None of the above
5. A manufacturer of stereo equipment introduces new models in the fall. Retail dealers are surveyed immediately after the Christmas selling season regarding their stock on hand of each piece of equipment.  It has been discovered that unless 40% of the new equipment ordered by the retailers in the fall had been sold by Christmas, immediate production cutbacks are needed.  The manufacturer has found that contacting all of the dealers after Christmas by mail is frustrating as many of them never respond.  This year 80 dealers were selected at random and telephoned regarding a new receiver.  It was discovered that 38% of those receivers had been sold.  Since 38% is less than 40%, does this mean that immediate production cutbacks are needed or can this difference of 2 percentage points be attributed to sampling?  Test at the 0.05 level.  Computed z = 0.37.
A: Cut back production
B: Do not cut back production
C: Cannot determine based on information given
D: None of the above
6. If 20 out of 50 students sampled live in a college dormitory, what is the estimated proportion of students at the University living in a dormitory?
A: 0.20
B: 0.40
C: 0.50
D: 0.60
7. Use the following to answer questions 7-11:

 

The average cost of tuition, room and board at small private liberal arts colleges is reported to be $8,500 per term, but a financial administrator believes that the average cost is higher.  A study conducted using 150 small liberal arts colleges showed that the average cost per term is $8,745 with a standard deviation of $1,200.  Let a = 0.05.

What is the null and alternative hypotheses for this study?

A: Null: m $9,000; alternative: m > $9,000
B: Null: m $9,000; alternative: m < $9,000
C: Null: m $8,500; alternative: m > $8,500
D: Null: m $8,500; alternative: m < $8,500
8. What is the critical z-value for this test?
A: + 1.96
B: 1.96
C: + 1.65
D: 1.65
9. What is the test statistic for this test?
A: 2.50
B: 0.204
C: -2.50
D: +2.50
10. What is the p-value for this test?
A: 0.0062
B: 0.0124
C: 0.0500
D: 0.4938
11. Based on the computed test statistic or p-value, what is our decision about the average cost?
A: Equal to $8,500
B: Greater than $8,500
C: Less than $8,500
D: Not equal to $8,500
12. Use the following to answer questions 12-15:

 

It is claimed that in a bushel of peaches less than ten percent are defective.  A sample of 400 peaches is examined and 50 are found to be defective.

What is the null hypothesis?

A: p 0.10
B: p 0.10
C: p 0.10
D: p < 0.10
13. What is the alternate hypothesis for a one-sided test?
A: p 0.10
B: p < 0.10
C: p 0.10
D: p = 0.10
14. What is the z-statistic?
A: 0.025
B: 0.278
C: 1.65
D: 1.67
15. If a = 0.025, what will be the decision?
A: Fail to reject the null and conclude the defects are not greater than 10%
B: Reject the null and conclude the defects are not greater than 10%
C: Reject the null and conclude the defects are greater than 10%
D: Fail to reject the null and conclude the defects are not less than 10%


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