Question

A researcher compares two compounds (1 and 2) used in the manufacture of car tires that are designed to reduce braking distances for SUVs equipped with the tires. SUVs equipped with tires using compound 1 have a mean braking distance of 6262 feet and a standard deviation of 10.610.6 feet. SUVs equipped with tires using compound 2 have a mean braking distance of 6868 feet and a standard deviation of 13.913.9 feet. Suppose that a sample of 7777 braking tests are performed for each compound. Using these results, test the claim that the braking distance for SUVs equipped with tires using compound 1 is shorter than the braking distance when compound 2 is used. Let μ1μ1 be the true mean braking distance corresponding to compound 1 and μ2μ2 be the true mean braking distance corresponding to compound 2. Use the 0.050.05 level of significance.

Step 1 of 4 : State the null and alternative hypotheses for the test.

Step 2 of 4: Compute the value of the test statistic. Round your answer to two decimal places.

Step 3 of 4: Determine the decision rule for rejecting the null
hypothesis H_{0}. Round the numerical portion of your
answer to two decimal places.

Step 4 of 4: Make the decision for the hypothesis test. Fail or reject to fail.

Answer #1

Let μ1 be the true mean braking distance corresponding to compound 1 and μ2 be the true mean braking distance corresponding to compound 2.

**STEP
1:** **NULL HYPOTHESIS H0:**

**ALTERNATIVE HYPOTHESIS Ha:
**

**STEP
2:** Test Statistics

The z-statistic is computed as follows:

**z= -3.01**

**STEP
3:** Based on the information provided, the
significance level is α=0.05, and the critical value for a
left-tailed test is zc=−1.64.

**STEP 4:** Since it is observed that
z=−3.012<z∗=−1.64, it is then concluded that *the null
hypothesis is rejected.*

*Decision: FAIL TO REJECT NULL HYPOTHESIS H0.*

A researcher compares two compounds (1 and 2) used in the
manufacture of car tires that are designed to reduce braking
distances for SUVs equipped with the tires. SUVs equipped with
tires using compound 1 have a mean braking distance of 6060 feet
and a standard deviation of 10.210.2 feet. SUVs equipped with tires
using compound 2 have a mean braking distance of 6262 feet and a
standard deviation of 9.09.0 feet. Suppose that a sample of 8989
braking tests...

A researcher compares two compounds (1 and 2) used in the
manufacture of car tires that are designed to reduce braking
distances for SUVs equipped with the tires. SUVs equipped with
tires using compound 1 have a mean braking distance of 62 feet and
a standard deviation of 10.6 feet. SUVs equipped with tires using
compound 2 have a mean braking distance of 6868 feet and a standard
deviation of 13.9 feet. Suppose that a sample of 77 braking tests...

A researcher compares two compounds (1 and 2) used in the
manufacture of car tires that are designed to reduce braking
distances for SUVs equipped with the tires. SUVs equipped with
tires using compound 1 have a mean braking distance of 5050 feet
and a standard deviation of 13.413.4 feet. SUVs equipped with tires
using compound 2 have a mean braking distance of 5858 feet and a
standard deviation of 10.510.5 feet. Suppose that a sample of 7373
braking tests...

A researcher compares two compounds (1 and 2) used in the
manufacture of car tires that are designed to reduce braking
distances for SUVs equipped with the tires. SUVs equipped with
tires using compound 1 have a mean braking distance of 74 feet and
a standard deviation of 7.8 feet. SUVs equipped with tires using
compound 2 have a mean braking distance of 77 feet and a standard
deviation of 7.3 feet. Suppose that a sample of 81 braking tests...

A researcher compares two compounds (1 and 2) used in the
manufacture of car tires that are designed to reduce braking
distances for SUVs equipped with the tires. SUVs equipped with
tires using compound 1 have a mean braking distance of 77 feet and
a standard deviation of 12.8 feet. SUVs equipped with tires using
compound 2 have a mean braking distance of 85 feet and a standard
deviation of 5.3 feet. Suppose that a sample of 33 braking tests...

A researcher compares two compounds (1 and 2) used in the
manufacture of car tires that are designed to reduce braking
distances for SUVs equipped with the tires. SUVs equipped with
tires using compound 1 have a mean braking distance of 78 feet and
a standard deviation of 14.9 feet. SUVs equipped with tires using
compound 2 have a mean braking distance of 86 feet and a standard
deviation of 5.9 feet. Suppose that a sample of 7979 braking tests...

A researcher compares two compounds (1 and 2) used in the
manufacture of car tires that are designed to reduce braking
distances for SUVs equipped with the tires. SUVs equipped with
tires using compound 1 have a mean braking distance of 53 feet and
a standard deviation of 8.2 feet. SUVs equipped with tires using
compound 2 have a mean braking distance of 59 feet and a standard
deviation of 12.1 feet. Suppose that a sample of 47 braking tests...

A researcher compares two compounds (1 and 2) used in the
manufacture of car tires that are designed to reduce braking
distances for SUVs equipped with the tires. SUVs equipped with
tires using compound 1 have a mean braking distance of 64 feet and
a standard deviation of 5.4 feet. SUVs equipped with tires using
compound 2 have a mean braking distance of 69 feet and a standard
deviation of 9.6 feet. Suppose that a sample of 76 braking tests...

A researcher compares two compounds (1 and 2) used in the
manufacture of car tires that are designed to reduce braking
distances for SUVs equipped with the tires. The mean braking
distance for SUVs equipped with tires made with compound 1 is 55
feet, with a population standard deviation of 5.6. The mean braking
distance for SUVs equipped with tires made with compound 2 is 60
feet, with a population standard deviation of 14.2. Suppose that a
sample of 69...

A researcher compares two compounds (1 and 2) used in the
manufacture of car tires that are designed to reduce braking
distances for SUVs equipped with the tires. SUVs equipped with
tires using compound 1 have a mean braking distance of 63 feet and
a standard deviation of 13.0 feet. SUVs equipped with tires using
compound 2 have a mean braking distance of 68 feet and a standard
deviation of 6.8 feet. Suppose that a sample of 76 braking tests...

ADVERTISEMENT

Get Answers For Free

Most questions answered within 1 hours.

ADVERTISEMENT

asked 8 minutes ago

asked 9 minutes ago

asked 11 minutes ago

asked 15 minutes ago

asked 31 minutes ago

asked 32 minutes ago

asked 47 minutes ago

asked 48 minutes ago

asked 55 minutes ago

asked 56 minutes ago

asked 57 minutes ago

asked 1 hour ago