Author: Anonymous

Which of the following experiments does NOT generate a continuous random variable?

The sampling distribution of the sample proportion

Refer to the Exhibit 3. What is the shape of the sampling distribution of the proportion?

A store owner is trying to construct the confidence interval for the proportion of customers who make a purchase. She observes that 25 customers made a purchase out of 50 customers who entered the store. What is the margin of error for the 90% confidence interval for the population proportion of customers who make a purchase? Please, consult the critical values in the table below. Recall that the subscript refers to the area on the right of the critical value in the corresponding distribution. Critical Value df Value — 1.28 — 1.65 49 1.30 49 1.68  

Refer to Exhibit 2. Now, assume that the Census data is not available. Based on the sample information, you find that the 97% confidence interval for the proportion of female gun owners is [0.12, 0.23]. When interpreting this interval, you would say that:

Based on the historical data, a mail-order company determined and now advertises that it ships 90% of its orders within three working days of receipt of the order. Correspondingly, for 10% of orders it takes more than three working days to be shipped. Last month the company received 10,000 orders. The company is planning an audit of 100 randomly chosen orders from last month. The random variable  represents the number of orders shipped within more than three working days in the sample of audited orders and follows the binomial distribution. You are asked to calculate the probability that, during the audit, 15 orders will reveal that it took more than three working days to get them shipped. What is the number of trials and the probability of success you will use to calculate this probability?

Exhibit 1 How did the challenge of high inflation in 2022 affect the spending patterns of the typical household? Let us think about the average annual household expenditures on food items away from home. Food away from home expenditures include spending at restaurants, take-out venues, and all other meals not prepared in one’s home. Let us assume that the data from the Consumer Expenditure Surveys shows that the annual household expenditures on food items away from home in 2022 followed the normal distribution with the average expenditure of $3,639 and the standard deviation of $736. A sample of 16 households was selected. The average annual expenditures on food items in the sample were $2,890 in 2022. Note: Please, note that the unit of observation is household in this exhibit. So, the sample size is equal to 16. You do NOT need to multiply it by the number of people to get the sample size. Reminder:

Refer to Exhibit 1. As mentioned earlier, assume that the study showed that the standard deviation of the serial interval of COVID-19 is 5 days which is treated as the sample standard deviation of COVID-19 serial interval obtained based on a sample of 16 COVID-19 patients. Assume that the serial interval of COVID- 19 is normally distributed in the population. Find the margin of error for the 90% confidence interval for the average serial interval? Please, consult the critical values in the table below. Recall that the subscript refers to the area on the right of the critical value in the corresponding distribution. Critical Value df Value — 1.28 — 1.645 15 1.34 15 1.75

Which of the following would be required for creating confidence intervals for the population proportion?

Refer to Exhibit 1. Thinking about a confidence interval for the average serial interval of COVID-19, which of the following situations will NOT allow us constructing a reliable confidence interval?