Please answer all parts in the same format as pictured. P=T=N=X=Degrees of freedom =S=Thanks **Challenge Activity: 6.2.2: Relating Confidence Intervals to Hypothesis Testing (One Sample)****Jump to level 1**An auto maker is interested in information about how long transmissions last. A sample of transmissions are run constantly and the number of miles before the transmission fails is recorded. The auto maker claims that the transmissions can run constantly for over 150,000 miles before failure. The results of the sample are given below.**Data Summary:**| Statistic | Value ||------------------------------------------|---------|| **Miles (1000s of miles)** | || Mean | 150.7 || Variance | 4.551 || Observations | 42 || Hypothesized Mean | 150 || df (Degrees of Freedom) | 41 || t Statistic | 2.17 || P(T<=t) one-tail | 0.018 || t Critical one-tail | 1.683 || P(T<=t) two-tail | 0.036 || t Critical two-tail | 2.02 || Confidence Level (95.0%) | 0.665 |The graph shows a bell-shaped curve centered around the mean value with t-distribution. The specific region highlighted shows the critical region for the hypothesis test. The x-axis represents t-values ranging from -3 to 3, while the y-axis represents the probability density.**Hypothesis Testing Criteria:**- **Null Hypothesis (H₀):** The mean number of miles before transmission failure is 150,000 miles.- **Alternative Hypothesis (H₁):** The mean number of miles before transmission failure is not 150,000 miles.**Conditions for Using a t-Distribution:**- The population is stated to be not skewed.- The sample size is larger than 30.**Statistical Calculations:**- $ n = \text{{number of samples}} = 42 $- $ \bar{x} = \text{{mean}} = 150.7 $- $ s = \text{{standard deviation}} = \sqrt{4.551} $- Degrees of Freedom $ (df) = n - 1 = 41 $By using the provided t-statistic and critical values, we

# P stands for Probability value which is shaded in graphical display. # T stands for test statistic…

Jump to level 1 A auto maker is interested in information about how long transmissions last. A sample of transmissions are run constantly and the number of miles before the transmission fails is recorded. The auto maker claims that the transmissions can run constantly for over 150,000 miles before failure. The results of the sample are given below. Miles (1000s of miles) Mean 150.7 Variance 4.551 Observations 42 Hypothesized Mean 150 df 41 t Stat 2.17 p= Ex: 1.234 P(T<=t) one-tail t Critical one-tail 0.018 1.683 -2 1 3 P(T<=t) two-tail t Critical two-tail 0.036 2.02 t = Ex: 1.234 Confidence Level(95.0%) 0.665 What condition is met for the use of a t-distribution? Pick The populationhs stated to be not skewed. n = Ex: 5 x = Ex: 1The sample size is larger than 30. Degrees of freedom = Ex: 5 S = Ex: 1.234

Jump to level 1 A auto maker is interested in information about how long transmissions last. A sample of transmissions are run constantly and the number of miles before the transmission fails is recorded. The auto maker claims that the transmissions can run constantly for over 150,000 miles before failure. The results of the sample are given below. Miles (1000s of miles) Mean 150.7 Variance 4.551 Observations 42 Hypothesized Mean 150 df 41 t Stat 2.17 p= Ex: 1.234 P(T<=t) one-tail t Critical one-tail 0.018 1.683 -2 1 3 P(T<=t) two-tail t Critical two-tail 0.036 2.02 t = Ex: 1.234 Confidence Level(95.0%) 0.665 What condition is met for the use of a t-distribution? Pick The populationhs stated to be not skewed. n = Ex: 5 x = Ex: 1The sample size is larger than 30. Degrees of freedom = Ex: 5 S = Ex: 1.234

Glencoe Algebra 1, Student Edition, 9780079039897, 0079039898, 2018

18th Edition

ISBN:9780079039897

Author:Carter

Publisher:Carter

Chapter10: Statistics

Section: Chapter Questions

Problem 25SGR

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Question

Please answer all parts in the same format as pictured. P= T= N= X= Degrees of freedom = S= Thanks

**Challenge Activity: 6.2.2: Relating Confidence Intervals to Hypothesis Testing (One Sample)**

**Jump to level 1**

An auto maker is interested in information about how long transmissions last. A sample of transmissions are run constantly and the number of miles before the transmission fails is recorded. The auto maker claims that the transmissions can run constantly for over 150,000 miles before failure. The results of the sample are given below.

**Data Summary:**

| Statistic | Value |
|------------------------------------------|---------|
| **Miles (1000s of miles)** | |
| Mean | 150.7 |
| Variance | 4.551 |
| Observations | 42 |
| Hypothesized Mean | 150 |
| df (Degrees of Freedom) | 41 |
| t Statistic | 2.17 |
| P(T<=t) one-tail | 0.018 |
| t Critical one-tail | 1.683 |
| P(T<=t) two-tail | 0.036 |
| t Critical two-tail | 2.02 |
| Confidence Level (95.0%) | 0.665 |

The graph shows a bell-shaped curve centered around the mean value with t-distribution. The specific region highlighted shows the critical region for the hypothesis test. The x-axis represents t-values ranging from -3 to 3, while the y-axis represents the probability density.

**Hypothesis Testing Criteria:**

- **Null Hypothesis (H₀):** The mean number of miles before transmission failure is 150,000 miles.
- **Alternative Hypothesis (H₁):** The mean number of miles before transmission failure is not 150,000 miles.

**Conditions for Using a t-Distribution:**

- The population is stated to be not skewed.
- The sample size is larger than 30.

**Statistical Calculations:**

- $ n = \text{{number of samples}} = 42 $
- $ \bar{x} = \text{{mean}} = 150.7 $
- $ s = \text{{standard deviation}} = \sqrt{4.551} $
- Degrees of Freedom $ (df) = n - 1 = 41 $

By using the provided t-statistic and critical values, we

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