Data on the weights (lb) of the contents of cans of diet soda versus the contents of cans of the regular version of the soda is summarized to the right. Assume that the two samples are independent simple random samples selected from normally distributed populations, and do not assume that the population standard deviations are equal. Complete parts (a) and (b) below. Use a 0.01 significance level for both parts. DietRegular μμ1μ2 n2424 x0.78797 lb0.80081 lb s0.00438 lb0.00741 lb ### Analysis of Soda Can Weights: Diet vs. RegularData on the weights (lb) of the contents of cans of diet soda versus the contents of cans of the regular version is summarized below. Assume the two samples are independent, simple random samples selected from normally distributed populations, and do not assume the population standard deviations are equal. A 0.01 significance level is used for both parts.#### Summary of Data:- **Mean (μ):** - Diet: $ \mu_1 = 0.78797 $ lb - Regular: $ \mu_2 = 0.80081 $ lb- **Sample size (n):** - Both Diet and Regular: $ n = 24 $- **Standard deviation (s):** - Diet: $ s = 0.00438 $ lb - Regular: $ s = 0.00741 $ lb### Hypothesis Testing#### (a) Test the Claim**Objective:** Determine if the mean weight of diet soda cans is less than that of regular soda.1. **Formulate Hypotheses:** - **A.** $ H_0: \mu_1 = \mu_2 $ (Null Hypothesis) - **H_1: \mu_1 < \mu_2 \) (Alternative Hypothesis)2. **Analysis Steps:** - **Test Statistic $ t $:** (Fill in the calculated value, rounded to two decimal places.) - **P-value:** (Fill in the calculated value, rounded to three decimal places.)3. **Conclusion:** - **Choices:** - **A:** Reject $ H_0 $, sufficient evidence to support $ \mu_1 < \mu_2 $. - **B:** Reject $ H_0 $, insufficient evidence. - **C:** Fail to reject $ H_0 $, sufficient evidence. - **D:** Fail to reject $ H_0 $, insufficient evidence.#### (b) Confidence Interval**Construct a confidence interval for the hypothesis test in part (a).**- **Interval:** Calculate and fill in: $ \text{lb} < \mu_1 - \mu_2 < \text{lb} $ (rounded to three decimal places).**Conclusion Based on Confidence Interval:**- Does it support the hypothesis

Answered: Data on the weights (lb) of the…

MATLAB: An Introduction with Applications

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

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Data on the weights (lb) of the contents of cans of diet soda versus the contents of cans of the regular version of the soda is summarized to the right. Assume that the two samples are independent simple random samples selected from normally distributed populations, and do not assume that the population standard deviations are equal. Complete parts (a) and (b) below. Use a 0.01 significance level for both parts.

	Diet	Regular
μ	μ1	μ2
n	24	24
x	0.78797 lb	0.80081 lb
s	0.00438 lb	0.00741 lb

### Analysis of Soda Can Weights: Diet vs. Regular

Data on the weights (lb) of the contents of cans of diet soda versus the contents of cans of the regular version is summarized below. Assume the two samples are independent, simple random samples selected from normally distributed populations, and do not assume the population standard deviations are equal. A 0.01 significance level is used for both parts.

#### Summary of Data:
- **Mean (μ):**
- Diet: $ \mu_1 = 0.78797 $ lb
- Regular: $ \mu_2 = 0.80081 $ lb
- **Sample size (n):**
- Both Diet and Regular: $ n = 24 $
- **Standard deviation (s):**
- Diet: $ s = 0.00438 $ lb
- Regular: $ s = 0.00741 $ lb

### Hypothesis Testing

#### (a) Test the Claim
**Objective:** Determine if the mean weight of diet soda cans is less than that of regular soda.

1. **Formulate Hypotheses:**
- **A.** $ H_0: \mu_1 = \mu_2 $ (Null Hypothesis)
- **H_1: \mu_1 < \mu_2 \) (Alternative Hypothesis)

2. **Analysis Steps:**
- **Test Statistic $ t $:** (Fill in the calculated value, rounded to two decimal places.)
- **P-value:** (Fill in the calculated value, rounded to three decimal places.)

3. **Conclusion:**
- **Choices:**
- **A:** Reject $ H_0 $, sufficient evidence to support $ \mu_1 < \mu_2 $.
- **B:** Reject $ H_0 $, insufficient evidence.
- **C:** Fail to reject $ H_0 $, sufficient evidence.
- **D:** Fail to reject $ H_0 $, insufficient evidence.

#### (b) Confidence Interval
**Construct a confidence interval for the hypothesis test in part (a).**

- **Interval:** Calculate and fill in: $ \text{lb} < \mu_1 - \mu_2 < \text{lb} $ (rounded to three decimal places).

**Conclusion Based on Confidence Interval:**
- Does it support the hypothesis

Features Features Normal distribution is characterized by two parameters, mean (µ) and standard deviation (σ). When graphed, the mean represents the center of the bell curve and the graph is perfectly symmetric about the center. The mean, median, and mode are all equal for a normal distribution. The standard deviation measures the data's spread from the center. The higher the standard deviation, the more the data is spread out and the flatter the bell curve looks. Variance is another commonly used measure of the spread of the distribution and is equal to the square of the standard deviation.

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$n subscript 1 equals 24 n subscript 2 equals 24 x with bar on top subscript 1 equals 0.78797 x with bar on top subscript 2 equals 0.80081 s subscript 1 equals 0.00438 s subscript 2 equals 0.00741$