I need help with what is blank and well explained please **Hypothesis Testing Using t-distribution**A random sample of 19 observations taken from a normally distributed population yielded a sample mean of 42.4 and a standard deviation of 8. The goal is to find the range for the *p-value* and the critical and observed values of *t* for each of the following hypothesis tests at a significance level of $\alpha = 0.01$.To determine the *p-value* range, use the *t* distribution table. Round all *t* values to three decimal places.### Test a**Null Hypothesis ($H_0$)**: $\mu = 46$**Alternative Hypothesis ($H_1$)**: $\mu < 46$- **Observed t Value ($t_{observed}$)**: -1.96- Determine the range for *p-value* as: `< p-value <`- Use the *t-distribution* table to fill in the *critical t* value ($t_{critical}$).### Test b**Null Hypothesis ($H_0$)**: $\mu = 46$**Alternative Hypothesis ($H_1$)**: $\mu \neq 46$- Determine the range for *p-value* as: `< p-value <`- Use the *t-distribution* table to determine values.This setup helps you understand hypothesis testing and the use of t-distribution in evaluating the statistical significance of your test results. **Hypothesis Testing with a Sample of Normally Distributed Data**A random sample of 19 observations taken from a normally distributed population produced a sample mean of 42.4 and a standard deviation of 8. The task is to find the range for the p-value and the critical and observed values of t for two different hypothesis tests using a significance level, α = 0.01.**Instructions:**- Use the t distribution table to find a range for the p-value.- Round your answers for the values of t to three decimal places.**Part a: Test the Hypothesis**- Null Hypothesis (H₀): μ = 46 - Alternative Hypothesis (H₁): μ < 46.To determine:1. The range for the p-value.2. The critical value of t (t_critical).3. The observed value of t (t_observed = -1.96 is provided).**Part b: Test the Hypothesis**- Null Hypothesis (H₀): μ = 46 - Alternative Hypothesis (H₁): μ ≠ 46.To determine:1. The range for the p-value.2. The critical value of t (t_critical).3. The observed value of t (not provided; calculate as needed).Use the given information and the appropriate statistical tools to complete the hypothesis testing for both scenarios.

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Description: I need help with what is blank and well explained please **Hypothesis Testing Using t-distribution**A random sample of 19 observations taken from a normally distributed population yielded a sample mean of 42.4 and a standard deviation of 8. The goal

given information: n=19 μ=46s=8x¯=42.4α=0.01 a) null and alternative: H0:μ=46H1:μ<46 test…

Math

Statistics

Arandom sample of 19 observations taken from a population that is normally distributed produced a sample mean of 42.4 and a standard deviation of 8. Find the range for the p-value and the critical and observed values of t for each of the following tests of hypotheses using, a = 0.01.

Arandom sample of 19 observations taken from a population that is normally distributed produced a sample mean of 42.4 and a standard deviation of 8. Find the range for the p-value and the critical and observed values of t for each of the following tests of hypotheses using, a = 0.01.

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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I need help with what is blank and well explained please

**Hypothesis Testing Using t-distribution**

A random sample of 19 observations taken from a normally distributed population yielded a sample mean of 42.4 and a standard deviation of 8. The goal is to find the range for the *p-value* and the critical and observed values of *t* for each of the following hypothesis tests at a significance level of $\alpha = 0.01$.

To determine the *p-value* range, use the *t* distribution table. Round all *t* values to three decimal places.

### Test a

**Null Hypothesis ($H_0$)**: $\mu = 46$

**Alternative Hypothesis ($H_1$)**: $\mu < 46$

- **Observed t Value ($t_{observed}$)**: -1.96
- Determine the range for *p-value* as: `< p-value <`
- Use the *t-distribution* table to fill in the *critical t* value ($t_{critical}$).

### Test b

**Null Hypothesis ($H_0$)**: $\mu = 46$

**Alternative Hypothesis ($H_1$)**: $\mu \neq 46$

- Determine the range for *p-value* as: `< p-value <`
- Use the *t-distribution* table to determine values.

This setup helps you understand hypothesis testing and the use of t-distribution in evaluating the statistical significance of your test results.

**Hypothesis Testing with a Sample of Normally Distributed Data**

A random sample of 19 observations taken from a normally distributed population produced a sample mean of 42.4 and a standard deviation of 8. The task is to find the range for the p-value and the critical and observed values of t for two different hypothesis tests using a significance level, α = 0.01.

**Instructions:**

- Use the t distribution table to find a range for the p-value.
- Round your answers for the values of t to three decimal places.

**Part a: Test the Hypothesis**

- Null Hypothesis (H₀): μ = 46
- Alternative Hypothesis (H₁): μ < 46.

To determine:

1. The range for the p-value.
2. The critical value of t (t_critical).
3. The observed value of t (t_observed = -1.96 is provided).

**Part b: Test the Hypothesis**

- Null Hypothesis (H₀): μ = 46
- Alternative Hypothesis (H₁): μ ≠ 46.

To determine:

1. The range for the p-value.
2. The critical value of t (t_critical).
3. The observed value of t (not provided; calculate as needed).

Use the given information and the appropriate statistical tools to complete the hypothesis testing for both scenarios.

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