The effectiveness of a new bug repellent is tested on 17 subjects for a 10 hour period. (Assume normally distributed population.) Based on the number and location of the bug bites, the percentage of surface area exposed protected from bites was calculated for each of the subjects. The results were as follows: T = 92, 8 = 12 The new repellent is considered effective if it provides a percent repellency of at least 90. Using a = 0.01, construct a hypothesis test with null hypothesis μ = 90 and alternative hypothesis > 90 to determine whether the mean repellency of the new bug repellent is greater than 90 by computing the following: (a) the degree of freedom (b) the critical t value (c) the test statistics

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**Study on Bug Repellent Effectiveness**

A new bug repellent was tested on 17 subjects over a 10-hour period. The percentage of skin surface protected from bites was recorded for each subject. The observed results were as follows:

- Mean (\(\overline{x}\)): 92
- Standard deviation (\(s\)): 12

**Objective:**
The repellent is deemed effective if it achieves a repellency rate of at least 90%. To test this, we use a hypothesis test with:

- Null Hypothesis (\(H_0\)): \(\mu = 90\)
- Alternative Hypothesis (\(H_1\)): \(\mu > 90\)

**Significance Level:**
- \(\alpha = 0.01\)

**Tasks:**

(a) **Degree of Freedom:** Calculate the degree of freedom needed for the test.

(b) **Critical \(t\) Value:** Determine the critical \(t\) value for the given significance level and degree of freedom.

(c) **Test Statistics:** Compute the test statistics to evaluate the effectiveness of the bug repellent.
Transcribed Image Text:**Study on Bug Repellent Effectiveness** A new bug repellent was tested on 17 subjects over a 10-hour period. The percentage of skin surface protected from bites was recorded for each subject. The observed results were as follows: - Mean (\(\overline{x}\)): 92 - Standard deviation (\(s\)): 12 **Objective:** The repellent is deemed effective if it achieves a repellency rate of at least 90%. To test this, we use a hypothesis test with: - Null Hypothesis (\(H_0\)): \(\mu = 90\) - Alternative Hypothesis (\(H_1\)): \(\mu > 90\) **Significance Level:** - \(\alpha = 0.01\) **Tasks:** (a) **Degree of Freedom:** Calculate the degree of freedom needed for the test. (b) **Critical \(t\) Value:** Determine the critical \(t\) value for the given significance level and degree of freedom. (c) **Test Statistics:** Compute the test statistics to evaluate the effectiveness of the bug repellent.
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