One cable company claims that it has excellent customer service. In fact, the company advertises that a technician will arrive within 30
 minutes after a service call is placed. One frustrated customer believes this is not accurate, claiming that it takes over 30
 minutes for the cable technician to arrive. The customer asks a simple random sample of 16
 other cable customers how long it has taken for the cable technician to arrive when they have called for one. The sample mean for this group is 33.4
 minutes with a standard deviation of 8.1
 minutes. Assume that the population distribution is approximately normal. Test the customer’s claim at the 0.10
 level of significance.
Step 2 of 3: Compute the value of the test statistic. Round your answer to three decimal places.

We are testing the customer's claim that it takes more than 30 minutes for a cable technician to arrive. To do this, we will perform a **one-sample t-test**. 

### Step 1: State the hypotheses
- **Null hypothesis (\(H_0\))**: The mean arrival time is 30 minutes, \( \mu = 30 \).
- **Alternative hypothesis (\(H_A\))**: The mean arrival time is greater than 30 minutes, \( \mu > 30 \).

This is a **right-tailed test** because the customer claims that the time is greater than 30 minutes.

### Step 2: Compute the test statistic

The test statistic for a one-sample t-test is calculated as:

\[
t = \frac{\bar{x} - \mu_0}{\frac{s}{\sqrt{n}}}
\]

Where:
- \( \bar{x} = 33.4 \) is the sample mean.
- \( \mu_0 = 30 \) is the hypothesized population mean.
- \( s = 8.1 \) is the sample standard deviation.
- \( n = 16 \) is the sample size.

Now, let's calculate the test statistic:

\[
t = \frac{33.4 - 30}{\frac{8.1}{\sqrt{16}}}
\]

Let me compute that for you.The value of the test statistic is approximately \( t = 1.679 \).

Would you like further details on this process or help with the next step of the hypothesis test?

Here are five related questions:
1. How do we determine the critical value for this test?
2. What is the p-value corresponding to this test statistic?
3. How does the sample size affect the test result?
4. What assumptions are made when conducting a t-test?
5. How can the test be modified for a two-tailed scenario?

**Tip:** Always ensure your sample size is sufficient to make the results reliable, especially when using small sample sizes.

One cable company claims that it has excellent customer service. In fact, the company advertises that a technician will arrive within 30 minutes after a service call is placed. One frustrated customer believes this is not accurate, claiming that it takes over 30 minutes for the cable technician to arrive. The customer asks a simple random sample of 16 other cable customers how long it has taken for the cable technician to arrive when they have called for one. The sample mean for this group is 33.4 minutes with a standard deviation of 8.1 minutes. Assume that the population distribution is approximately normal. Test the customer’s claim at the 0.10 level of significance.

Test a customer's claim using a one-sample t-test to determine if the cable technician's arrival time exceeds 30 minutes. The sample of 16 customers shows a mean arrival time of 33.4 minutes with a standard deviation of 8.1 minutes. Learn hypothesis testing at a 0.10 significance level.

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