103 A researcher was interested in comparing the response ti

103) A researcher was interested in comparing the response times of two different cab companies. Companies A and B were each called at 50 randomly selected times. The calls to company A were made independently of the calls to company B. The response times for each call were recorded. The summary statistics were as follows: Use a 0.02 significance level to test the claim that the mean response time for company A is the same as the mean response time for company B. Use the P-value method of hypothesis testing. Objective: (93) *Test Claim About Two Means (Indep Samples) 104) Two types of flares are tested and their burning times (in minutes) are recorded. The summary statistics are given below. Use a 0.05 significance level to test the claim that the two samples are from populations with the same mean. Use the traditional method of hypothesis testing. Objective: (9.3) *Test Claim About Two Means (Indep Samples)

Solution

H0: mu1=mu2

Ha:mu1 not equals mu 2

(Two sided test)

z for 98% CI= 2.33
declare p larger than alpha=0.02 not significant.

mean1 eq: 7.6 (variance= 2.22) (se= 0.2107)
mean2 eq: 6.9 (variance= 2.89) (se= 0.2404)

Probability that var1 p=0.82042 (left: 0.1796; double: 0.3592)

Difference between means:
M1-M2=7.6-6.9=0.7
sd=3.1379; se=0.3197
98% CI of difference:
-0.0437 <0.7< 1.4437
t-difference: 2.19
df-t: 95.8; p= 0.98437
(left p: 0.0156; two sided: 0.0312)

Difference not significant at 2%

Hence two means are equal

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2)

H0: mu1=mu2

Ha:mu1 not equals mu 2

(Two sided test)

z for 95% CI= 1.96
declare p larger than alpha=0.05 not significant.

mean1 eq: 19.4 (variance= 2.22) (se= 0.2519)
mean2 eq: 15.1 (variance= 0.64) (se= 0.1265)

Probability that var1 p=0.00012 (left: 0.9999; double: 0.0002)

Difference between means:
M1-M2=19.4-15.1=4.3
sd=2.0031; se=0.2818
95% CI of difference:
3.7476 <4.3< 4.8524
t-difference: 15.257
df-t: 50; p= 1
(left p: 0; two sided: 0)

As p value for two sided is 0, reject null hypothesis.

There is significant difference between the two means.