Question

1. a car company says that the mean gas mileage for its luxury sedan is at least 23 miles per gallon (mpg). you believe the claim is incorrect and find that a random sample of 7 cars has a mean gas mileage of 20 mpg and a standard deviation of 4 mpg. at α = 0.05, test the companys claim. assume the population is normally distributed.

which sampling distribution should be used and why?
a. use a t - sampling distribution because the population is normal, and σ is known.
b. use a normal sampling distribution because the population is normal, and σ is known.
c. use a t - sampling distribution because n < 30.
d. use a normal sampling distribution because n > 30.
e. use a normal sampling distribution because the population is normal, and σ is unknown.
f. use a t - sampling distribution because the population is normal, and σ is unknown.
state the appropriate hypotheses to test.
a. h₀: μ = 23
hₐ: μ ≠ 23
b. h₀: μ ≤ 23
hₐ: μ > 23
c. h₀: μ ≠ 23
hₐ: μ = 23
d. h₀: μ ≠ 23
hₐ: μ = 23
what is the value of the standardized test statistic?
the standardized test statistic is (round to two decimal places as needed.)

Explanation:

Step1: Determine the sampling distribution

Since the population is normally distributed and the population standard deviation \(\sigma\) is unknown (we are given the sample standard deviation \(s = 4\)), we use the \(t -\)sampling distribution.

Step2: State the hypotheses

The company claims \(\mu\geq23\). We want to test if the claim is incorrect. The null hypothesis \(H_{0}\) is the claim we are testing against. So \(H_{0}:\mu = 23\) and \(H_{1}:\mu<23\)

Step3: Calculate the \(t -\)test statistic

The formula for the \(t -\)test statistic is \(t=\frac{\bar{x}-\mu}{s/\sqrt{n}}\)
Here, \(\bar{x} = 20\), \(\mu = 23\), \(s = 4\), \(n = 7\)

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Answer:

The standardized test statistic is approximately \(-1.98\)