I need the answer for the question. Thank you. ### Hypothesis Testing for Changes in Smoking AgeThe mean age when smokers first start is 13 years old with a population standard deviation of 2 years. A researcher thinks that the smoking age has significantly changed since the invention of ENDS—electronic nicotine delivery systems. A survey of smokers of this generation was done to see if the mean age has changed. The sample of 33 smokers found that their mean starting age was 12.1 years old. Do the data support the claim at the 5% significance level?#### Formulate the Hypotheses**Null Hypothesis (H₀):**The mean starting age of smokers has not changed and is still 13 years.- $ H₀: \mu = 13 $ years**Alternative Hypothesis (H₁):**The mean starting age of smokers has changed from 13 years.- $ H₁: \mu \neq 13 $ years#### Calculations**Test Statistic:**To determine if the mean age has significantly changed, we'll calculate the z-score using the formula for the test statistic in hypothesis testing:- $ z = \frac{\bar{x} - \mu}{\sigma / \sqrt{n}} $Where:- $ \bar{x} $ is the sample mean (12.1 years),- $ \mu $ is the population mean (13 years),- $ \sigma $ is the population standard deviation (2 years),- $ n $ is the sample size (33).**Critical Values:**For a two-tailed test at the 5% significance level, the critical values are the z-scores that correspond to the extreme 2.5% tails of the normal distribution. These can be found in z-tables or using statistical software.#### Decision RuleCompare the calculated z-score with the critical values:- If $ |z| $ > z-critical, reject the null hypothesis $ H₀ $.- If $ |z| $ ≤ z-critical, fail to reject the null hypothesis $ H₀ $.#### Result Interpretation- Based on the z-score and the critical values, decide whether to reject the null hypothesis.- If we reject $ H₀ $, it suggests that the mean age smokers first start is significantly different from 13 years.- If we fail to reject $ H₀ $, it suggests there is no significant difference

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Description: I need the answer for the question. Thank you. ### Hypothesis Testing for Changes in Smoking AgeThe mean age when smokers first start is 13 years old with a population standard deviation of 2 years. A researcher thinks that the smoking age has signif

From the provided information, Mean (µ) = 13 years Population standard deviation (σ) = 2 years…

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The mean age when smokers first start is 13 years old with a population standard deviation of 2 years. A researcher thinks that smoking age has significantly changed since the invention of ENDS-electronic nicotine Heliver N Syste ms A suvey of smokers of this generation vwas done to seo if the m

The mean age when smokers first start is 13 years old with a population standard deviation of 2 years. A researcher thinks that smoking age has significantly changed since the invention of ENDS-electronic nicotine Heliver N Syste ms A suvey of smokers of this generation vwas done to seo if the m

MATLAB: An Introduction with Applications

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Author:Amos Gilat

Publisher:Amos Gilat

Chapter1: Starting With Matlab

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I need the answer for the question. Thank you.

### Hypothesis Testing for Changes in Smoking Age

The mean age when smokers first start is 13 years old with a population standard deviation of 2 years. A researcher thinks that the smoking age has significantly changed since the invention of ENDS—electronic nicotine delivery systems. A survey of smokers of this generation was done to see if the mean age has changed. The sample of 33 smokers found that their mean starting age was 12.1 years old. Do the data support the claim at the 5% significance level?

#### Formulate the Hypotheses

**Null Hypothesis (H₀):**
The mean starting age of smokers has not changed and is still 13 years.
- $ H₀: \mu = 13 $ years

**Alternative Hypothesis (H₁):**
The mean starting age of smokers has changed from 13 years.
- $ H₁: \mu \neq 13 $ years

#### Calculations

**Test Statistic:**
To determine if the mean age has significantly changed, we'll calculate the z-score using the formula for the test statistic in hypothesis testing:

- $ z = \frac{\bar{x} - \mu}{\sigma / \sqrt{n}} $

Where:

- $ \bar{x} $ is the sample mean (12.1 years),
- $ \mu $ is the population mean (13 years),
- $ \sigma $ is the population standard deviation (2 years),
- $ n $ is the sample size (33).

**Critical Values:**
For a two-tailed test at the 5% significance level, the critical values are the z-scores that correspond to the extreme 2.5% tails of the normal distribution. These can be found in z-tables or using statistical software.

#### Decision Rule

Compare the calculated z-score with the critical values:
- If $ |z| $ > z-critical, reject the null hypothesis $ H₀ $.
- If $ |z| $ ≤ z-critical, fail to reject the null hypothesis $ H₀ $.

#### Result Interpretation

- Based on the z-score and the critical values, decide whether to reject the null hypothesis.
- If we reject $ H₀ $, it suggests that the mean age smokers first start is significantly different from 13 years.
- If we fail to reject $ H₀ $, it suggests there is no significant difference

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