Question

Based on an indication that mean daily car rental rates may be higher for Toronto than for Montreal, a survey of eight car rental companies in Toronto is taken, and the sample mean car rental rate is $50, with a standard deviation of $4. Further, suppose a survey of nine car rental companies in Montreal results in a sample mean of $42 and a standard deviation of $4. Use a = 0.05 to test to determine whether the average daily car rental rates in Toronto are higher than those in Montreal. Assume car rental rates are normally distributed and the population variances are equal. Round your answer to 2 decimal places. Observed t = The decision is to The average daily car rental rates in Toronto are significantly than those in Montreal.

Answer 1

Below are the null and alternative Hypothesis,
Null Hypothesis, H0: μ1 = μ2
Alternative Hypothesis, Ha: μ1 > μ2

Rejection Region
This is right tailed test, for α = 0.05 and df = n1 + n2 - 2 = 15
Critical value of t is 1.753.
Hence reject H0 if t > 1.753

Pooled Variance
sp = sqrt((((n1 - 1)*s1^2 + (n2 - 1)*s2^2)/(n1 + n2 - 2))*(1/n1 + 1/n2))
sp = sqrt((((8 - 1)*4^2 + (9 - 1)*4^2)/(8 + 9 - 2))*(1/8 + 1/9))
sp = 1.9437

Test statistic,
t = (x1bar - x2bar)/sp
t = (50 - 42)/1.9437
t = 4.12

P-value Approach
P-value = 0
As P-value < 0.05, reject the null hypothesis.

The decision is to reject H0

are significantly more than those in Montreal