MGMT2262 Worksheet #5

MGMT2262

Worksheet #5

1) Surveys indicate that adults spend an average of 4 hours per day between watching TV and listening to radio with a standard deviation of 1.2 hours. If a sample of 50 adults is chosen, what is the probability the average amount of time this group spends doing the above activities is more than 4.3 hours? (0.0384)

2) Suppose the sample size is 100 instead. What does the probability in question 1 change to? (0.0062)

3) A survey of 100 people was taken to see how much they spend on fast food per week. For the 100 people, the average was $15.14 with a standard deviation of $2.54.

a) Construct a 95% confidence interval of the average amount that people spend per week on fast food (14.64 < m < 15.64)

b) Suppose the level of confidence was increased to 99%. Does the confidence interval become narrower or wider? (14.49 < m < 15.79; wider)

c) Suppose the sample size was 200 instead of 100 and the sample mean and standard deviation remained at $15.14 and $2.54 respectively. Would a 95% confidence interval be narrower or wider than the one in part a? (14.79 < m < 15.49; narrower)

d) Suppose the sample size was 100 but the standard deviation was $5.08. If the sample mean remained at $15.14, would a 95% confidence interval be narrower or wider than the one in part a? (14.14 < m < 16.14; wider)

e) Suppose they wanted to conduct another study. If they use the standard deviation of $2.54 and they wanted the margin or error to be 50 cents and the level of confidence to be 95%, what would the sample size need to be? (n = 100)

4) Suppose a focus group of 8 people is held and the amount they spend on gambling per week is recorded:

21.51	14.97	15.77	17.49
15.04	11.26	18.09	14.77

The researchers have no prior information to work with. However, analysis of the data indicated it is normally distributed. Construct a 95% confidence interval of the average amount people spend on gambling per week. (13.60 < m < 18.62)

5) Suppose the researchers wanted to conduct another study. If they use the standard deviation from the data in question 4 and they want a margin of error of 25 cents at a 95% level of confidence, what would the sample size be? (552)

6) Suppose the researchers cannot afford more than 300 surveys. What would the margin of error need to be if they use the standard deviation from question 4 and a 95% level of confidence? (34 cents)

7) Average daily sales in a store are normally distributed with a mean of $1000 and standard deviation of $250. An advertising campaign was conducted to see if daily sales could be increased. After the campaign was conducted, 14 days of sales were sampled and average daily sales per day in this period was $1120. Test that the sales increased significantly at the 5% level of significance. (Z = 1.796; reject Ho; conclude campaign increased sales)

8) Programmers at a software company average 2.2 coding mistakes per 1000 lines of code with a standard deviation of 1.3 mistakes. They underwent a training program to learn how to reduce the number of mistakes. After the program, 50 sets of 1000 lines of code were sampled and the average number of mistakes for each set was 1.8. Test that the number of mistakes is significantly lower at a 1% level of significance. ( Z = -2.1757; do not reject Ho; conclude program did not significantly reduce the average number of mistakes)

9) The amount of milk in a carton averages 1 litre with a standard deviation of 12.5 millilitres. The cartons are measured 100 at a time to ensure that specifications are being met. In one such sample, the average was 1002 millilitres. Test that the specifications are being met at the 3% level of significance. (Z = 1.6; do not reject Ho; conclude specifications are being met)

10) For the above questions, calculate the p-value. Find, if possible, a level of significance between 1% and 10% in which the opposite verdict would have been reached. (question 7: p-value = 0.0359 – level of significance between 1% and 3.59%; question 8: p-value = 0.0146 – level of significance between 1.46% and 10%; question 9: p-value = 0.1096; no level of significance since the p-value is greater than 10%)

11) For the hypothesis in question 9, construct a 97% confidence interval of the average amount of milk in a carton. If we used the confidence interval to test the hypothesis, why would we have reached the same conclusion? (999.2875 ml < m 1004.7125; the hypothesis mean of 1000 falls in this confidence interval)

12) It is estimated that semi-retired people work an average of 25 hours per week and is normally distributed. A focus group of 8 semi-retired people is held and the number of hours per week they work is recorded:

Test the hypothesis at the 5% level of significance. (t = -2.8505; reject Ho; conclude semi-retired people do not work an average of 25 hours per week)

13) For the above question, estimate where the p-value lies. (p-value is between 0.02 and 0.05)

14) Construct a 95% confidence interval of the average amount of time that semi-retired people work per week and interpret the interval. If this interval were used to test the hypothesis in question 12, why would the same conclusion be reached?

(16.3 < m < 24.2; with 95% confidence, semi-retired people work between 16.3 and 24.2 hours per week; the hypothesis mean of 25 falls outside this confidence interval)