S A coin-operated drink machine was designed to discharge a mean of 9 fluid ounces of coffee per cup. In a test of the machine, the discharge amounts in 20 randomly chosen cups of coffee from the machine were recorded. The sample mean and sample standard deviation were 9.12 fluid ounces and 0.18 fluid ounces, respectively. If we assume that the discharge amounts are approximately normally distributed, is there enough evidence, to conclude that the population mean discharge, μ, differs from 9 fluid ounces? Use the 0.05 level of significance. Perform a two-tailed test. Then complete the parts below. Carry your intermediate computations to three or more decimal places. (If necessary, consult a list of formulas.) (a) State the null hypothesis Ho and the alternative hypothesis H₁. Ho :D H₁ :0 (b) Determine the type of test statistic to use. (Choose one) ▼ (c) Find the value of the test statistic. (Round to three or more decimal places.) (d) Find the two critical values. (Round to three or more decimal places.) Dand (e) Can we conclude that the mean discharge differs from fluid ounces? OYes No μ X OD O X S Do ローロ OSO 020 Р ê 믐 S OO ? 9 199 M

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**Transcription for Educational Website:**

A coin-operated drink machine was designed to discharge a mean of 9 fluid ounces of coffee per cup. In a test of the machine, the discharge amounts in 20 randomly chosen cups of coffee from the machine were recorded. The sample mean and sample standard deviation were 9.12 fluid ounces and 0.18 fluid ounces, respectively.

If we assume that the discharge amounts are approximately normally distributed, is there enough evidence to conclude that the population mean discharge, \( \mu \), differs from 9 fluid ounces? Use the 0.05 level of significance.

Perform a two-tailed test. Then complete the parts below.

Carry your intermediate computations to three or more decimal places. (If necessary, consult a list of formulas.)

(a) State the null hypothesis \( H_0 \) and the alternative hypothesis \( H_1 \).

\( H_0: \) [ ]

\( H_1: \) [ ]

(b) Determine the type of test statistic to use.

(Choose one) ▼

(c) Find the value of the test statistic. (Round to three or more decimal places.)

[ ]

(d) Find the two critical values. (Round to three or more decimal places.)

[ ] and [ ]

(e) Can we conclude that the mean discharge differs from 9 fluid ounces?

☐ Yes ☐ No

---

### Explanation of Icons and Tools:

The section includes an array of symbols within a selection box, often used in hypothesis testing:

- Sample mean (\( \bar{x} \))
- Population standard deviation (\( \sigma \))
- Sample standard deviation (\( s \))
- Population proportion (\( p \))
- Sample proportion (\( \hat{p} \))

These tools aid in selecting relevant statistical measures for solving hypothesis testing problems.
Transcribed Image Text:**Transcription for Educational Website:** A coin-operated drink machine was designed to discharge a mean of 9 fluid ounces of coffee per cup. In a test of the machine, the discharge amounts in 20 randomly chosen cups of coffee from the machine were recorded. The sample mean and sample standard deviation were 9.12 fluid ounces and 0.18 fluid ounces, respectively. If we assume that the discharge amounts are approximately normally distributed, is there enough evidence to conclude that the population mean discharge, \( \mu \), differs from 9 fluid ounces? Use the 0.05 level of significance. Perform a two-tailed test. Then complete the parts below. Carry your intermediate computations to three or more decimal places. (If necessary, consult a list of formulas.) (a) State the null hypothesis \( H_0 \) and the alternative hypothesis \( H_1 \). \( H_0: \) [ ] \( H_1: \) [ ] (b) Determine the type of test statistic to use. (Choose one) ▼ (c) Find the value of the test statistic. (Round to three or more decimal places.) [ ] (d) Find the two critical values. (Round to three or more decimal places.) [ ] and [ ] (e) Can we conclude that the mean discharge differs from 9 fluid ounces? ☐ Yes ☐ No --- ### Explanation of Icons and Tools: The section includes an array of symbols within a selection box, often used in hypothesis testing: - Sample mean (\( \bar{x} \)) - Population standard deviation (\( \sigma \)) - Sample standard deviation (\( s \)) - Population proportion (\( p \)) - Sample proportion (\( \hat{p} \)) These tools aid in selecting relevant statistical measures for solving hypothesis testing problems.
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