A manufacturer makes ball bearings that are supposed to have a mean weight of 30 g. A retailer suspects that the mean weight is actually less than 30 g. The mean weight for a random sample of 16 ball bearings is 28.6 g with a standard deviation of 4.4 g. Assume the population standard deviation is not known.**How many populations?**- O 2- O 1**What is the parameter?**- O Proportion- O Mean- O Variance- O Standard Deviation- O Difference between Means **What is the test statistic?**1. **t-test for two means (independent samples):** \[ t = \frac{(\bar{x}_1 - \bar{x}_2) - (\mu_1 - \mu_2)}{\sqrt{\frac{s_1^2}{n_1} + \frac{s_2^2}{n_2}}} \]2. **z-test for two proportions:** \[ z = \frac{(\hat{p}_1 - \hat{p}_2) - (p_1 - p_2)}{\sqrt{\frac{\bar{p} \cdot \bar{q}}{n_1} + \frac{\bar{p} \cdot \bar{q}}{n_2}}} \]3. **F-test for two variances:** \[ F = \frac{s_1^2}{s_2^2} \]4. **z-test for two means (independent samples with known variances):** \[ z = \frac{(\bar{x}_1 - \bar{x}_2) - (\mu_1 - \mu_2)}{\sqrt{\frac{\sigma_1^2}{n_1} + \frac{\sigma_2^2}{n_2}}} \]5. **t-test for one mean:** \[ t = \frac{\bar{x} - \mu}{\frac{s}{\sqrt{n}}} \]6. **Chi-square test:** \[ \chi^2 = \frac{(n-1)^2 \cdot s^2}{\sigma^2} \]7. **z-test for one proportion:** \[ z = \frac{\hat{p} - p}{\sqrt{\frac{p \cdot q}{n}}} \]8. **t-test for dependent samples (paired samples):** \[ t_d = \frac{\bar{x} - \bar{x}_d}{\frac{s_d}{\sqrt{n}}} \]9. **t-test for pooled variance (independent samples):** \[ t = \frac{(\bar{x}_1 - \bar{x}_2) - (\mu

H0 : μ= 30 H1: μ < 30 (Left tail ) ============================== Answer: 1…

A manufacturer makes ball bearings that are supposed to have a mean weight of 30 g. A retailer suspects that the mean weight is actually less than 30 g. The mean weight for a random sample of 16 ball bearings is 28.6 g with a standard deviation of 4.4 g. Assume the population standard deviation is not known. How many populations? 02 01 What is the parameter? O Proportion O Mean O Variance Standard Deviation O Difference between Means

A manufacturer makes ball bearings that are supposed to have a mean weight of 30 g. A retailer suspects that the mean weight is actually less than 30 g. The mean weight for a random sample of 16 ball bearings is 28.6 g with a standard deviation of 4.4 g. Assume the population standard deviation is not known. How many populations? 02 01 What is the parameter? O Proportion O Mean O Variance Standard Deviation O Difference between Means

MATLAB: An Introduction with Applications

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

Chapter1: Starting With Matlab

Section: Chapter Questions

Problem 1P

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Concept explainers

Estimation

A new framework of data analysis where the new statistical methods are used for interpreting the results and analyzing the data is known as estimation in statistics.

Question

A manufacturer makes ball bearings that are supposed to have a mean weight of 30 g. A retailer suspects that the mean weight is actually less than 30 g. The mean weight for a random sample of 16 ball bearings is 28.6 g with a standard deviation of 4.4 g. Assume the population standard deviation is not known.

**How many populations?**

- O 2
- O 1

**What is the parameter?**

- O Proportion
- O Mean
- O Variance
- O Standard Deviation
- O Difference between Means

**What is the test statistic?**

1. **t-test for two means (independent samples):**

\[
t = \frac{(\bar{x}_1 - \bar{x}_2) - (\mu_1 - \mu_2)}{\sqrt{\frac{s_1^2}{n_1} + \frac{s_2^2}{n_2}}}
\]

2. **z-test for two proportions:**

\[
z = \frac{(\hat{p}_1 - \hat{p}_2) - (p_1 - p_2)}{\sqrt{\frac{\bar{p} \cdot \bar{q}}{n_1} + \frac{\bar{p} \cdot \bar{q}}{n_2}}}
\]

3. **F-test for two variances:**

\[
F = \frac{s_1^2}{s_2^2}
\]

4. **z-test for two means (independent samples with known variances):**

\[
z = \frac{(\bar{x}_1 - \bar{x}_2) - (\mu_1 - \mu_2)}{\sqrt{\frac{\sigma_1^2}{n_1} + \frac{\sigma_2^2}{n_2}}}
\]

5. **t-test for one mean:**

\[
t = \frac{\bar{x} - \mu}{\frac{s}{\sqrt{n}}}
\]

6. **Chi-square test:**

\[
\chi^2 = \frac{(n-1)^2 \cdot s^2}{\sigma^2}
\]

7. **z-test for one proportion:**

\[
z = \frac{\hat{p} - p}{\sqrt{\frac{p \cdot q}{n}}}
\]

8. **t-test for dependent samples (paired samples):**

\[
t_d = \frac{\bar{x} - \bar{x}_d}{\frac{s_d}{\sqrt{n}}}
\]

9. **t-test for pooled variance (independent samples):**

\[
t = \frac{(\bar{x}_1 - \bar{x}_2) - (\mu

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