Solve the Problem Using Technology, Perform the Following Hypothesis Test: at the 5

question 46

Multiple Choice

Solve the problem. Use the critical-value approach.
-A machine that fills soda bottles is supposed to fill them to a mean volume of 16.2 fluid ounces. A random sample of 20 filled bottles produced the following volumes in fluid ounces: $$\begin{array}{l}\begin{array} { l l l l l l l l l l } 16.3 & 15.9 & 16.7 & 15.3 & 17.1 & 16.4 & 3.9 & 15.9 & 16.2 & 3.4 \\16.4 & 8.2 & 15.5 & 16.5 & 16.0 & 16.3 & 15.8 & 16.7 & 16.5 & 15.5\end{array}\\\text { These data are summarized on the following histogram: }\end{array}$$

Using technology, perform the following hypothesis test: at the 5% significance level,determine Whether the fill volume is less than the supposed value. Comment on the appropriateness of the Test.

• A) Test statistic: \(t = - 1.8063\); Critical value: \(- 2.0921\). Since the test statistic is greater than the critical value, do not reject the null hypothesis \(\mathrm { H } _ { 0 } : \mu = 16.2 \mathrm { oz }\). There is insufficient evidence to conclude that the fill volume is below \(16.2\) oz. The conclusion is on sound statistical ground.
• B) Test statistic: \(t = - 1.8063\); Critical value: \(- 1.7254\). Since the test statistic is less than the critical value, do not reject the null hypothesis \(\mathrm { H } _ { 0 } : \mu =\) \(16.2 \mathrm { oz }\). There is insufficient evidence to conclude that the fill volume is below \(16.2\) oz. However, the data exhibits 3 outliers. Elimination of these outliers may alter the conclusion.
• C) Test statistic: \(t = - 1.8063\); Critical value; \(- 2.0921\). Since the test statistic is greater than the critical value, do not reject the null hypothesis \(\mathrm { H } _ { 0 } : \mu = 16.2 \mathrm { oz }\). There is insufficient evidence to conclude that the fill volume is below \(16.2\) oz. However, the data exhibits 3 outliers. Elimination of these outliers may alter the conclusion.
• D) Test statistic: \(t = - 1.8063\); Critical value: \(- 1.729\). Since the test statistic is less than the critical value, reject the null hypothesis \(\mathrm { H } _ { 0 } : \mu = 16.2 \mathrm { oz }\). There is sufficient evidence to conclude that the fill volume is below \(16.2 \mathrm { oz }\). However, the data exhibits 3 outliers. Elimination of these outliers may alter the conclusion.

---

Definitions:

The Taking of Christ

A famous Baroque painting by Caravaggio, capturing the moment of Jesus Christ's arrest in the Garden of Gethsemane.

Dramatic Reworking

The process of adapting original works, such as literature or art, into new forms, often to convey different perspectives or contemporary relevance.

Giotto

An Italian painter and architect from the Late Middle Ages, credited with contributing significantly to the Renaissance by creating more lifelike and emotional artworks.

Canonical Iconography

Standardized and widely recognized visual symbols or themes within an artistic or religious tradition that convey specific meanings.