QUESTION 1

1. Consider a Z test for p with the hypotheses:

• H₀: p = 0.6
• H_A: p?0.6

Suppose the test statistic is z = 2.78.

Given that P(Z

1. 0.0027
2. 0.0054
3. 0.6
4. 0.9973

QUESTION 2

Suppose that in a random sample of 90 of a city's houses, 51 are occupied by renters. Using the formula in the course notes, what is a 95% confidence interval for the true proportion of the city's houses that are occupied by renters?

1. [0.481, 0.653]
2. [0.464, 0.669]
3. [0.282, 0.441]
4. [-1.96, 1.96]

QUESTION 3

Suppose a company takes a random sample of its casual and full-time employees and asks them to anonymously report whether they feel valued, with the results summarised in the table below:

\f. nip12 10 . n1(1 - p1) 2 10 . n2P2 2 10 . n2(1 - P2) 210\f\fFeel valued Do not feel Total valued Full-time 38 17 55 Casual 24 27 51 Total 62 44 106Party Labor Liberal/National Green Other Total II Preference: II Frequency: 71 81 20 28 200Proportion Test (N Outcomes) Proportions - Party Level Count Proportion Labor Observed 71 0.355 Expected 66.000 0.330 Liberal/National Observed 81 0.405 Expected 82.000 0.410 Green Observed 20 0.100 Expected 20.000 0.100 Other Observed 28 0.140 Expected 32.000 0.160x2 Goodness of Fit X2 df 0.891 W 0.828PLab = 0.33 PLN = 0.41 PG = 0.1 Po = 0.16PLab = 0.33 PLN = 0.41 PG = 0.1 po 0.16PLab = 0.25 PLN = 0.25 PG = 0.25 Po = 0.25Feel valued Do not feel Total valued Full-time 38 17 55 Casual 24 27 51 Total 62 44 106H0: There is an association between employment status and whether the employee feels valued HA: There is no association between employment status and whether the employee feels valued H0: There is no association between employment status and whether the employee feels valued HA: There is an association between employment status and whether the employee feels valued Let ; and g be the sample proportions of fulltime and casual employees who feel valued, respectively. we HAzlatE Let if; and g be the sample proportions of fulltime and casual employees who feel valued, respectively. Hotlal are Suppose a company takes a random sample of its casual and full-time employees and asks them to anonymously report whether they feel valued, with the results summarised in the table below: - Feel valued Do not feel valued -z-- Based on the output from a chi-squared test of independence presented below, what is the value of the test statistic? x1 Tests Value df p x2 5.291 \"I 0.021 N 106 O 0.021 O 5.330 O 4.422 O 5.291 Suppose a random sample of parts from three different factories was collected and tested for faults, with the results summarised in the table below: -m-- _n m Based on the output from a chi-squared test of independence presented below, what is an appropriate conclusion? Contingency Tables Contingency Tables Defective Factory not defective defective Total Factory A Observed 222 18 240 Expected 221 .667 18.333 240.000 Factory B Observed 226 '14 240 Expected 221 .667 18.333 240.000 Factory C Observed 217 23 240 Expected 221 .667 18.333 240.000 Total Observed 665 55 720 Expected 665.000 55.000 720.000 x2 Tests Value df p x2 2.402 2 0.301 N 720