Question

question 1
2 pts
express the null hypothesis and the alternative hypothesis in symbolic form. use the correct symbol for the indicated parameter.
carter motor company claims that its new sedan, the libra, will average better than 23 miles per gallon in the city. use μ, the true average mileage of the libra.
○ h₀: μ > 23
h₁: μ ≤ 23
○ h₀: μ < 23
h₁: μ ≥ 23
○ h₀: μ = 23
h₁: μ > 23
○ h₀: μ = 23
h₁: μ < 23
question 2
2 pts
assume that the data has a normal distribution and the number of observations is greater than fifty. find the critical z value used to test a null hypothesis.
α = 0.1 for a two - tailed test.
○ ±1.4805
○ ±2.33
○ ±2.052

Explanation:

Step1: Identify hypotheses for Question 1

Null hypothesis ($H_0$) is neutral ($\mu=23$); alternative ($H_1$) matches claim ($\mu>23$).

Step2: Find critical z for Question 2

Two-tailed $\alpha=0.1$: split $\alpha$ into two tails ($0.05$ each). Critical z for $0.95$ cumulative probability is $\pm1.645$.

Answer:

Question 1: $H_0: \mu = 23$, $H_1: \mu > 23$
Question 2: $\pm1.645$ (Note: If the last option was $\pm1.645$, that is the correct one; the visible options may have a typo, but standard critical z for $\alpha=0.1$ two-tailed is $\pm1.645$)