Q7. Use the following information to answer questions 7 - 8:

In a sample of 250 Vancouverites, it is found that, on average, they hold a consumer non-mortgage debt balance of $38,588, with a standard deviation of $21,965. Based on census data, the average annual income of Vancouverites is $43,911. Does the average amount of debt exceed the average annual income amount from the census?

Fill in the blanks to construct the correct null and alternate hypotheses.

H₀: [ Select ] ["p", "p-hat", "", "y-bar"] [ Select ] ["<", "=", ">", ""] [ Select ] ["$38,588", "$43,911"]

H_A: [ Select ] ["p", "p-hat", "", "y-bar"] [ Select ] ["<", "=", ">", ""] [ Select ] ["$38,588", "$43,911"]

Q8. Using alpha = 0.01, what would the critical value be if the hypothesis test were one-sided?

Using alpha = 0.01, what would the critical value be if the hypothesis test were two-sided?

Answer as positive values to three decimal places.

Q9. The confidence interval for the sample proportion of tech companies that fail in the first five years is (0.319, 0.481). If you were to conduct a hypothesis test (using the corresponding alpha value) to determine if the proportion of tech companies that fail in the first five years is significantly different from 0.5, what would your decision be? Fill in the blanks to make the following sentences correct.

[ Select ] ["Fail to reject H0.", "Reject H0."] The proportion of tech companies that fail in the first five years [ Select ] ["is significantly different", "is not significantly different"] from 0.5.

Q10. Use the following information to answer questions 10 - 11:

In a random sample of 40 people who work in Vancouver, the average commute time for people who use an active method of transportation (bike or walk) is analyzed. Assume that the distribution is approximately Normal. A hypothesis test is done to determine if the commute time issignificantly less than 20 minutes using the hypotheses below:

H₀: average commute time for people who work in Vancouver = 20 minutes

H_A:average commute time for people who work in Vancouver <20 minutes

The test statistic found was -2.780. What would the p-value for this hypothesis test be? Answer to four decimal places. Q11. If the t critical value is -2.708, what would the decision be? Fill in the blanks to make the following sentences correct.

[ Select ] ["Fail to reject H0.", "Reject H0."] The average active commute time (walk or bike) is [ Select ] ["significantly", "not significantly"] less than 20 minutes.

Q12. In a random sample of 40 people who work in Vancouver, the average commute time by car is 30 minutes with a standard deviation of 4 minutes. Assume that the distribution is approximately Normal. What minimum sample size is needed for the margin of error of a 99% confidence interval to be at most 1 minute? Answer as a whole number. Use Excel to get precise values.

Q14. Match each of the following:

Group of answer choices

80 % confidence level

[ Choose ] Is used when alpha = 0.01 and the test is two-sided Is used when alpha = 0.01 and the test is one-sided Has a z critical value of 1.280 Corresponds to a critical value of about 2 Is used when alpha = 0.10 and the test is two-sided

90 % confidence level

[ Choose ] Is used when alpha = 0.01 and the test is two-sided Is used when alpha = 0.01 and the test is one-sided Has a z critical value of 1.280 Corresponds to a critical value of about 2 Is used when alpha = 0.10 and the test is two-sided

95 % confidence level

[ Choose ] Is used when alpha = 0.01 and the test is two-sided Is used when alpha = 0.01 and the test is one-sided Has a z critical value of 1.280 Corresponds to a critical value of about 2 Is used when alpha = 0.10 and the test is two-sided

98 % confidence level

[ Choose ] Is used when alpha = 0.01 and the test is two-sided Is used when alpha = 0.01 and the test is one-sided Has a z critical value of 1.280 Corresponds to a critical value of about 2 Is used when alpha = 0.10 and the test is two-sided

99% confidence level

[ Choose ] Is used when alpha = 0.01 and the test is two-sided Is used when alpha = 0.01 and the test is one-sided Has a z critical value of 1.280 Corresponds to a critical value of about 2 Is used when alpha = 0.10 and the test is two-sided