Z scores and the Area under the Normal Curve

a. Find the proportion of observations (area under the curve) from a standard normal distribution that satisfies each of the following statements:

i. Z < 2.78

ii. Z > -0.64

iii. -0.64

b. Find the value of the standard normal variable Z that satisfies each of the following conditions:

i. The value of Z with 38% of observations falling below it;

ii. The value of Z with 26% of observations falling above it.

c. Suppose the variable that represents the monthly time (in minutes) TV news has spent covering terrorism stories has an approximate normal distribution, with a mean of 520 minutes and a standard deviation of 233 minutes

i. What proportion of TV news spend at least 600 minutes covering terrorism stories?

ii. What proportion of TV news spends between 430 and 515 minutes on terrorism news?

iii. What is the monthly time spent covering terrorism news with 5% of TV news falling below it (i.e. what is the raw score (minutes) that corresponds to a probability close to 0.05)?

d. The distribution of immigrant family size in Australia is skewed to the right, with a µ=7.6 and σ = 6.3. These values of the population are known to you as the researcher who takes a sample of immigrant families from the population of Australian immigrants in order to estimate mean immigrant family size. If you select a random sample of 125 families:

i. What is the appropriate sampling distribution and why? Calculate the standard error for the sampling distribution

ii. Find the probability that your sample mean is greater than 6

2. Confidence Intervals and Hypothesis Tests

a. A sociologist uses a simple random sample to survey 450 college students. She finds that the mean amount of confidence in federal police is 4 (measured on a scale of 1-10 where 1 is the lowest confidence and 10 is the highest confidence). The sample variance, s², of the variable "confidence in the federal police" was 1.8.

i. Construct a 95% confidence interval for the mean level of confidence in federal police. Interpret this interval

ii. Another sociologist says that he knows that in the population from which this sample is drawn, the mean level of confidence in federal police is 5.6. Carry out an appropriate statistical test to examine the null hypothesis. Interpret your results

b. A random sample of 720 Queensland residents were asked what the most important priority is for the Australian Federal Government. 378 people chose "Maintaining order in the nation" as their first choice.

i. Construct a 95% confidence interval for the proportion of people who picked "maintaining order in the nation" as their first choice. Interpret this.

ii. Suppose you found out that the proportion of people in the population was actually 0.5. That is, 50% of the population thought that "maintaining order" should be our government's highest priority. Using the data above, perform a hypothesis test that determines if the sample is significantly different from the population. Make sure you use the appropriate estimate of the population proportion (as specified under the null hypothesis) in constructing the standard error. Interpret your findings

3. Confidence Intervals, Hypothesis Tests, and Chi Square

a. A random sample of 72 Brisbane adults report that they spend an average $560 per year on disaster preparedness supplies with a standard deviation of $33.

i. Identify and describe the correct probability distribution and explain why this is appropriate

ii. Construct a 99% confidence interval to estimate the population mean for disaster preparedness supplies spending in Brisbane as a whole. Fully interpret the interval

iii. Assume that we know that the official amount of money spent by the population of Queensland as a whole is µ = $485. Is the sample significantly different from the Queensland average?

b. Social Science Researchers are trying to understand what types of attitudes are related to reporting signs of terrorism to authorities. A random sample of Australians were surveyed about a range of attitudes related to terrorism. Below is a contingency table showing the distribution of respondent's political identification and whether they would report suspected terrorist activity to police.

i. Is there a statistically significant relationship between these variables. You can use the table below for your working.

ii. Compute the column percentages to determine the pattern of the relationship. Which group is more likely to report suspected terrorist activity to police?