The magazine randomly selects 16 owners of the car and ask them to measure how far the car can travel on a full charge. The mean distance traveled by these 16 cars was 510 miles with a standard deviation of 20 miles. Test the hypothesis that the mean distance the car can travel on a single charge is greater than 500 miles. Use a 0.05 level of significance. (Assume that the distances the car can travel on one charge are normally distributed.)
part D E
Q5
A company has developed an electric car they say can travel over 500
miles on a single charge. A consumer car magazine wants to test this claim. The
magazine randomly selects 16 owners of the car and ask them to measure how far
the car can travel on a full charge. The mean distance traveled by these 16 cars was
510 miles with a standard deviation of 20 miles. Test the hypothesis that the mean
distance the car can travel on a single charge is greater than 500 miles. Use a 0.05
level of significance. (Assume that the distances the car can travel on one charge are
(a) State the null and alternative hypothesis.
(b) Will this be a right-tailed, left-tailed, or two-tailed test?
(c) Calculate the test statistic assuming the null hypothesis is true.
T =
x − µ
√s
n
=
(d) Use the test statistic to calculate the P-value for the test.
P − value =
(e) Does the data provide enough evidence to conclude that, at the 5% significance
level, the mean distance this car can travel with a full charge is greater than
500 miles?
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