Questions: Determine the confidence coefficient (decision rule) for the following situation (round your answer to 2 decimal points. In cases where you have two confidence coefficients, provide one of the two possible answers): HO: μ=4.55, HA: μ ≠ 4.55, n=35, α=0.05

Determine the confidence coefficient (decision rule) for the following situation (round your answer to 2 decimal points. In cases where you have two confidence coefficients, provide one of the two possible answers):
HO: μ=4.55, HA: μ ≠ 4.55, n=35, α=0.05

Transcript text: Determine the confidence coefficient (decision rule) for the following situation (round your answer to 2 decimal points. In cases where you have two confidence coefficients, provide one of the two possible answers): \[ \text { HO: } \mu=\$ 4.55, H A: \mu \neq \$ 4.55, n=35, \alpha=0.05 \]

Solution

Solution Steps

To determine the confidence coefficient for the given hypothesis test, we need to find the critical value for a two-tailed test with a significance level of 0.05. This involves using the standard normal distribution (Z-distribution) since the sample size is large (n=35).

Step 1: Determine the Critical Value for a Two-Tailed Test

Given the significance level $\alpha = 0.05$, we need to find the critical value for a two-tailed test. This involves finding the value $z$ such that the area under the standard normal curve to the left of $z$ is $1 - \frac{\alpha}{2}$.

Step 2: Calculate the Critical Value

Using the standard normal distribution, the critical value $z$ for a two-tailed test with $\alpha = 0.05$ is: \[ z = \text{norm.ppf}(1 - \frac{\alpha}{2}) = \text{norm.ppf}(1 - 0.025) \approx 1.9599 \]

Step 3: Round the Critical Value

We round the critical value to two decimal points: \[ z \approx 1.96 \]