Question

Q1) A random sample of 10 travel brochures showed sample mean cost of an 8-day cruise to the Bahamas $1,978. (1st class, double occupancy). The sample standard deviation was $250. An independent random sample of 12 travel brochures showed mean cost of a comparable 8 day cruise to Mexico $2,150 with sample standard deviation $275. Test to see if the population mean costs for the two types of cruises are different. Use a 1% significance level.

Step 1: Ho: Ha:

Step 2
Step 3
Step 4

Step 5

Q2) A random sample of 100 students at a high school was asked whether they would ask their father or mother for help with a homework assignment in science. A second sample of 100 different students was asked the same question for an assignment in history. If 43 students in the first sample and 47 students in the second sample replied that they turned to their mother rather than their father for help, test the claim whether the difference between the proportions is due to chance. Use α = 0.10. [8.4]

Step 1: Ho: Ha:
Step 2:
Step 3:

Step 4:

Step 5:

Answer 1

Answer:

1.

Given,

Ho : u1 - u2 = 0

Ha : u1 - u2 != 0

test statistic t = (x1 - x2)/sqrt(s1^2/n1 + s2^2/n2)

substitute values

= (1978 - 2150)/sqrt(250^2/10 + 275^2/12)

= - 1.54

degree of freedom = n1 + n2 - 2 = 10 + 12 - 2 = 20

Critical value = t(alpha/2 , df) = 2.845

Reject Ho, if |t| > tcrit

Here we observe that, | t | < t crit , so we fail to reject Ho.

So we don't have enough evidence to support the claim.

2.

Ho : p1-p2 = 0

Ha : p1-p2 != 0

p1 = x1/n1 = 43/100 = 0.43

p2 = x2/n2 = 47/100 = 0.47

p^ = (p1 + p2)/(n1 + n2)

substitute values

= (47 + 43)/(100 + 100)

= 0.45

test statistic z = (p1 - p2)/sqrt(pq(1/n1 + 1/n2))

substitute values

= (0.47 - 0.43)/sqrt(0.45(1-0.45)*(1/100 + 1/100))

= 0.568

Critical value = 1.645

Here we observe that, test statistic < critical value, so we fail to reject Ho.

So there is no sufficient evidence to support the claim.