MGMT2263 Tutorial Sheet #4

1) A museum conducted a survey of 200 of its members and 200 of the general public telling them about new upcoming exhibits. After telling a respondent about the exhibits, they asked how likely it would be for the person to visit the museum within the following 12 months. These were the results:

	Member	Non-member	Total
Likely to visit	144	115	259
Not likely	56	85	141
Total	200	200	400

Are members more likely to visit new exhibits than non-members? Test at a 5% level of significance. (Z = 3.035; conclude members are more likely to visit)

2) Is there a level of significance between 1% and 10% that could have been chosen in which the opposite verdict could have been reached? (no since the p-value is less than 0.01)

3) Construct a 95% confidence interval of the difference in the percentage of members and non-members who will visit. Interpret the interval. (5.24% < p(members) – p(non-members) < 23.76%; the percentage of members who will visit new exhibits ranges from 5.24% to 23.76% more than the percentage of non-members)

4) In a deli, 3 checkouts were examined to see if there was any significant difference in the amount people spent at each checkout; 6 receipts were sampled from each checkout. These were the results:

Counter 1	Counter 2	Counter 3
14.00	17.25	17.45
11.56	16.48	16.89
15.36	14.68	14.25
17.94	16.24	15.82
17.75	15.43	19.42
19.08	16.27	16.25

Analysis of the data indicates each group is normally distributed. If we assume the variances of the 3 counters are equal, is there any significant difference in the average amount spent at each counter? (F = 0.236; conclude no significant difference)

5) Conduct the appropriate test to confirm the equality of variances among the 3 counters. (H = 10.18; conclude the variances are equal)

6) Conduct Tukey’s test on the data to confirm the ANOVA results. (D = 2.9806; all differences between the sample means are less than this)

7) Construct a 95% confidence interval of the average difference between the counter with the largest average and that with the smallest. Why is this confidence interval consistent with the results of ANOVA? (-1.72 < m3 - m1 < 3.18; m3 - m1 = 0 falls inside the confidence interval)

8) A factory wanted to compare production between its day, afternoon and night shifts. It has 5 lines. They sampled 5 hours worth of production from each line and measured the number of widgets built per hour. These were the results:

	Day	Afternoon	Night
Line 1	31	25	35
Line 2	33	26	33
Line 3	28	24	30
Line 4	30	29	28
Line 5	28	26	27

Analysis of the data from each shift indicates it is normally distributed.

a) Is there any significant difference in production between the 3 shifts? (F = 5.7546; conclude there is a significant difference)

b) Is there any significant difference in production between the 5 lines? (F = 1.5521; conclude there is no significant difference)

c) Between which shifts is there a significant difference? (afternoon and night)

d) Construct a 95% confidence interval of the average difference in production between the night and afternoon shifts (1.2 < m_night - m_afternoon < 8; the afternoon shifts produces between 1.2 and 8 more widgets per hour on average than the afternoon shift)

9) A researcher examined annual incomes by age groups and education levels. A survey had the following results (in thousands):

	< 30	30 to 54	55 and over
High school	18.2	20.8	25.4
	20.6	25.4	26.3
	21.3	27.3	29.7
Some PS	19.6	23.4	24.7
	25.3	26.3	26.2
	27.3	27.5	27.3
Complete PS	20.4	30.2	40.2
	25.6	31.4	45.6
	29.7	35.4	51.2

a) Does income depend on age? Test at a 5% level of significance. (F = 19.6059; conclude income depends on age)

b) Does income depend on education level? Test at a 5% level of significance. (F = 26.3252; conclude income depends on education)

c) Is there significant interaction between age and education? Test at a 5% level of significance. (F = 6.545; conclude there is significant interaction)