Please show how to find the test statistic. **Title: Statistical Analysis of Microwave Popcorn Popping Efficiency****Introduction:**Josh conducted an experiment to determine the optimal power and time settings for microwave popcorn. His aim was to achieve a result where fewer than 11% of the popcorn kernels remained unpopped. After various trials, he found that setting the microwave to power 9 for 4 minutes yielded the best results.**Part A: Error Analysis**Josh concluded this popping method achieved his goal of fewer than 11% unpopped kernels. If, in reality, the method does not work that well, the error Josh made is a **Type I error** (False positive).**Part B: Testing the Hypothesis**To verify the method's success, Josh performed additional tests by popping 8 more bags of popcorn at the same setting. The following are the percentages of unpopped kernels from these tests: - 12.4%, 2.9%, 8.6%, 8.1%, 13.4%, 3.2%, 2.7%, 9.5%**Research Question:**Does this data support Josh's hypothesis that the average percentage of unpopped kernels is fewer than 11%?**Hypotheses:**To determine this, we formulate the null and alternative hypotheses as follows:- **Null hypothesis ($H_0$)**: $ \mu \geq 11 $- **Alternative hypothesis ($H_A$)**: $ \mu < 11 $ **Choose the Correct Hypotheses:**- **A.** $H_0: \mu = 11 $ $ H_A: \mu < 11 $ (Correct)- B. $H_0: \mu \neq 11 $ $ H_A: \mu = 11 $- C. $H_0: \mu = 11 $ $ H_A: \mu \neq 11 $- D. $H_0: \mu = 11 $ $ H_A: \mu > 11 $- E. $H_0: \mu \leq 11 $ $ H_A: \mu = 11 $- F. $H_0: \mu > 11 $ $ H_A: \mu = 11 $**Calculate the Test Statistic:**Using the collected data, calculate

Given: No. of bags, n=8 Percentage of unpopped kernels (X) 12.4 2.9 8.6 8.1 13.4 3.2…

Answered: Calculate the test statistic. t-0…

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Calculate the test statistic. t-0 (Round to three decimal places as needed.)

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Concept explainers

Confidence Intervals

When we calculate intervals in probability and statistics, it can be simply termed as finding out a confidence interval. The confidence interval is usually calculated from the data set which is observed. The value of the parameter that needs to be calculated is present here only.

Question

Please show how to find the test statistic.

**Title: Statistical Analysis of Microwave Popcorn Popping Efficiency**

**Introduction:**
Josh conducted an experiment to determine the optimal power and time settings for microwave popcorn. His aim was to achieve a result where fewer than 11% of the popcorn kernels remained unpopped. After various trials, he found that setting the microwave to power 9 for 4 minutes yielded the best results.

**Part A: Error Analysis**
Josh concluded this popping method achieved his goal of fewer than 11% unpopped kernels. If, in reality, the method does not work that well, the error Josh made is a **Type I error** (False positive).

**Part B: Testing the Hypothesis**
To verify the method's success, Josh performed additional tests by popping 8 more bags of popcorn at the same setting. The following are the percentages of unpopped kernels from these tests:

- 12.4%, 2.9%, 8.6%, 8.1%, 13.4%, 3.2%, 2.7%, 9.5%

**Research Question:**
Does this data support Josh's hypothesis that the average percentage of unpopped kernels is fewer than 11%?

**Hypotheses:**
To determine this, we formulate the null and alternative hypotheses as follows:
- **Null hypothesis ($H_0$)**: $ \mu \geq 11 $
- **Alternative hypothesis ($H_A$)**: $ \mu < 11 $

**Choose the Correct Hypotheses:**
- **A.** $H_0: \mu = 11 $ $ H_A: \mu < 11 $ (Correct)
- B. $H_0: \mu \neq 11 $ $ H_A: \mu = 11 $
- C. $H_0: \mu = 11 $ $ H_A: \mu \neq 11 $
- D. $H_0: \mu = 11 $ $ H_A: \mu > 11 $
- E. $H_0: \mu \leq 11 $ $ H_A: \mu = 11 $
- F. $H_0: \mu > 11 $ $ H_A: \mu = 11 $

**Calculate the Test Statistic:**
Using the collected data, calculate

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