Question

A1A Tires claims that its tires last longer than tires manufactured by its main competitor, YYZ Tires. A consumer group studied the lifespans of tires manufactured by each manufacturer. The lifespans of a random sample of 10 tires from each manufacturer, in thousands of miles, are recorded.

Assume that the population standard deviation of the lifespan for tires manufactured by A1A Tires is 3 thousand miles, while the population standard deviation of the lifespan for tires manufactured by YYZ Tires is 5 thousand miles, and assume that the lifespans of both companies' tires are normally distributed. Let A1A Tires be the first sample, and let YYZ Tires be the second sample.

The consumer group conducts a two-mean hypothesis test at the 0.05 level of significance, to test if there is evidence that A1A Tires' claim is true.

(a) H0:μ1=μ2; Ha:μ1>μ2, which is a right-tailed test.

A1A Tires	YYZ Tires
50	46
47	45
43	46
47	35
47	36
45	28
45	41
45	38
38	41
45	39

The above table gives the lifespans of a random sample of 10 tires from each manufacturer, in thousands of miles.

(b) Use a TI-83, TI-83 Plus, or TI-84 calculator to test if there is evidence that A1A Tires' claim is true. Identify the test statistic, z, and p-value from the calculator output. Round your test statistic to two decimal places and your p-value to three decimal places.

NOTE: When entering the population standard deviations, enter them as single digits 3 and 5. (Do not include the extra zeros for thousands.)

Provide your answer below:

test statistic = , p-value =

Answer 1

Using TI 84 calculator STAT>EDIT > enter the data Again STAT>TESTS>2Sample Z test>Enter the data The results are as following 2-SIMPZ Test H1>Hz z=3.091259024 p=9.9661667E-4 X1=45.2 X2=39.5 Sx1=3.15524255 2-SMP2Test 111 >u2 1X2=39.5 Sx1=3. 15524255 Sx2=5.64210363 ni=10 n2=10

Test hypothesis are Họ: Al-u2 = 0 Hu1-112 > 0 Test statistic z=3.09 p-value =P(23.09)=0.000997 =0.0010 Since p-value <0.05 hence reject the null hypothesis