Question

According to a study done in 2013, the average age of a first-time home buyer in Canada was 29.6 years old. A researcher believes this number has increased since that time. A large random sample of Canadian first-time homebuyers is selected to test this claim. a. Determine what population parameter is being tested: μ: population mean b. Determine if the alternative hypothesis is a left-tailed, right-tailed, or two-tailed test: < : left-tailed > : right-tailed ≠ : two-tailed 2. H0: μ = 18 kg H1: μ > 18 kg Level of significance: α = 0.025 Sample size: n = 36 Test statistic: t = 2.305 Unknown population standard deviation T-Distribution Table a. Determine the critical value(s) for the proposed hypothesis test. ± Round to three decimal places if necessary b. Conclude whether to reject the null hypothesis or not based on the test statistic. Reject Fail to Reject c. State the decision error type that is possible. Type I Error Type II Error 3. The restaurant manager is testing the bartender's ability to pour 45 mL of spirits correctly into a mixed drink. The manager has the bartender pour water into 12 shot glasses to test their ability to pour the correct amount of spirits: 48 45 44 43 46 47 42 46 47 45 47 49 Note: The data appears to be approximately normally distributed. Test the bartender's ability to pour 45 mL at the 5% level of significance. T-Distribution Table a. Calculate the sample mean and standard deviation. x̄ = Round to three decimal places if necessary s = Round to three decimal places if necessary b. Calculate the test statistic. t = Round to three decimal places if necessary c. Determine the critical value(s) for the hypothesis test. ± Round to three decimal places if necessary d. Conclude whether to reject the null hypothesis or not based on the test statistic. Reject Fail to Reject

According to a study done in 2013, the average age of a first-time home buyer in Canada was 29.6 years old. A researcher believes this number has increased since that time. A large random sample of Canadian first-time homebuyers is selected to test this claim.

a. Determine what population parameter is being tested:
μ: population mean

b. Determine if the alternative hypothesis is a left-tailed, right-tailed, or two-tailed test:
< : left-tailed
> : right-tailed
≠ : two-tailed

2. H0: μ = 18 kg
H1: μ > 18 kg
Level of significance: α = 0.025
Sample size: n = 36
Test statistic: t = 2.305
Unknown population standard deviation
T-Distribution Table

a. Determine the critical value(s) for the proposed hypothesis test.
±
Round to three decimal places if necessary

b. Conclude whether to reject the null hypothesis or not based on the test statistic.
Reject
Fail to Reject

c. State the decision error type that is possible.
Type I Error
Type II Error

3. The restaurant manager is testing the bartender's ability to pour 45 mL of spirits correctly into a mixed drink. The manager has the bartender pour water into 12 shot glasses to test their ability to pour the correct amount of spirits:

48
45
44
43
46
47
42
46
47
45
47
49

Note: The data appears to be approximately normally distributed.

Test the bartender's ability to pour 45 mL at the 5% level of significance.
T-Distribution Table

a. Calculate the sample mean and standard deviation.
x̄ =
Round to three decimal places if necessary
s =
Round to three decimal places if necessary

b. Calculate the test statistic.
t =
Round to three decimal places if necessary

c. Determine the critical value(s) for the hypothesis test.
±
Round to three decimal places if necessary

d. Conclude whether to reject the null hypothesis or not based on the test statistic.
Reject
Fail to Reject

Added by Hector T.