Question

The cost of a wedding has skyrocketed in recent years. As a result, many couples are opting to have their weddings in the Caribbean. A Caribbean vacation resort recently advertised that the cost of a Caribbean wedding was less than $10 000. Listed below is the total cost (in $ thousands) for a sample of eight Caribbean weddings:

$10.0

$9.4

$9.9

$9.4

$9.4

$9.1

$10.9

$10.7

a. State the null hypothesis and the alternate hypothesis. (Enter the final answers in thousands of dollars.)

H₀: μ ≥           

H₁: μ <           

b. State the decision rule for 0.05 significance level. (Negative answer should be indicated by a minus sign. Round the final answer to 3 decimal places.)

Reject H₀ if t <            .

c. Compute the value of the test statistic. (Negative answer should be indicated by a minus sign. Round the final answer to 3 decimal places.)

Value of the test statistic           

d. At the 0.05 significance level, is it reasonable to conclude the mean wedding cost is less than $10,000 as advertised?

(Click to select)  Reject  Do not reject  H₀. There is  (Click to select)  enough  not enough  evidence to conclude that the cost is less than $10,000.

5) nxt qustn

A shopping centre wants to examine the amount of space required for parking. Studies indicated that 62% of staff and shoppers use public transportation. A survey of 1,002 was taken, and 560 responded that they used public transportation.

a. State the null hypothesis and the alternate hypothesis. Round the final answers to 2 decimal places.

H₀: p =           

H₁: p ≠            

b. State the decision rule for 0.05 significance level. (Negative answer should be indicated by a minus sign. Round the final answers to 2 decimal places.)

Reject H₀ if z >   or z <  .

c. Compute the value of the test statistic. (Negative answer should be indicated by a minus sign. Round the final answer to 2 decimal places.)

Value of the test statistic            

d. At the 0.05 significance level, is it reasonable to conclude that the survey results indicate a change?

(Click to select)  Do not reject  Reject  H₀. There is  (Click to select)  enough  not enough  evidence to indicate that the results have changed.

Answer 1

a)

   

b) df = 8 - 1 = 7

At alpha = 0.05, the critical value is -t_0.05,7 = -1.895

Reject H₀, if t < -1.895

c) = (10000 + 9400 + 9900 + 9400 + 9400 + 9100 + 10900 + 10700)/8 = 9850

s = sqrt(((10000 - 9850)^2 + (9400 - 9850)^2 + (9900 - 9850)^2 + (9400 - 9850)^2 + (9400 - 9850)^2 + (9100 - 9850)^2 + (10900 - 9850)^2 + (10700 - 9850)^2)/7) = 656.832

The test statistic is

Since the test statistic value is not less than the critical value(-0.646 > -1.895), so we should not reject the null hypothesis.

Do not reject H₀. There is not enough evidence to conclude that the cost is less than $10,000.

5) a)

        

b) At alpha = 0.05, the critical values are +/- z_0.025 = +/- 1.96

Reject H₀ if z < -1.96 or z > 1.96

c) = 560/1002 = 0.56

The test statistic is

  

d) Since the test statistic value is less than the negative critical value(-3.91 < -1.96), so we should reject the null hypothesis.

Reject H₀. There is enough evidence to indicate that the results have changed.