Suppose that Mairin has knit a collection of wool‑blend infinity scarves that she wants to sell in her Etsy shop for $28.00 each. However, she is worried that if the average price of comparable scarves is less than $28.00, hers would be less likely to sell.Mairin selected a random sample of 9 similar hand‑knit, wool‑blend infinity scarves, and their prices are as follows. $21.75,$24.00,$27.25,$29.95,$23.00,$26.00,$27.80,$33.50,$27.00$21.75,$24.00,$27.25,$29.95,$23.00,$26.00,$27.80,$33.50,$27.00 Use a left‑tailed one‑sample ?t‑test to determine whether the average price of hand‑knit, wool‑blend infinity scarves sold on Etsy is less than $28.00. Assume that the prices of all comparable scarves are normally distributed. Mairin should (reject, accept, fail to accept) her null hypothesis. There is (sufficient, no, insufficient) evidence that the mean price of hand‑knit, wool‑blend infinity scarves is (greater than, different from, less than, equal two) $28.00. **One-Sample t-Test Requirements and Hypothesis Selection**When conducting a one-sample t-test, it is essential to ensure that certain requirements are met for the test to be valid. Consider the following options and select the most appropriate one:1. **No**, Mairin selected a normally distributed random sample, but she does not know the population standard deviation.2. **Yes**, Mairin selected a random sample that is normally distributed and contains no outliers.3. **No**, Mairin selected a random sample from a normally distributed population, but her sample is too small.4. **Yes**, Mairin selected a random sample from a normally distributed population, and her sample contains no outliers.Next, you need to choose the appropriate null hypothesis ($H_0$) and alternative hypothesis ($H_1$) for the test.**Hypotheses:**- **$H_0$:** - $\mu = 28.00$ - $\bar{x} = 26.69$ - $\mu = 26.69$ - $\bar{x} = 28.00$- **$H_1$:** - $\bar{x} = 26.69$ - $\mu < 26.69$ - $\bar{x} < 28.00$ - $\mu < 28.00$**Calculation:**Calculate the t-test statistic and round your answer to three decimal places. Enter your solution in the provided box:$ t = \_\_\_\_\_\_\_\_\_ $ Use a *t*-distribution table to find a range of possible *P*-values for this test.- ○ 0.15 < *P* < 0.20- ○ 0.10 < *P* < 0.15- ○ 0.05 < *P* < 0.10- ● 0.20 < *P* < 0.25Complete the conclusion of this test. Use a significance level of α = 0.10.Mairin should [Dropdown] her null hypothesis. There is [Dropdown] evidence that the mean price of hand-knit, wool-blend infinity scarves is [Dropdown] $28.00.

Yes, Mairin selected a random sample from a normally distributed population, and her sample contains…

Answered: Have the requirements for a one-sample…

MATLAB: An Introduction with Applications

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

Chapter1: Starting With Matlab

Section: Chapter Questions

Problem 1P

See similar textbooks

Related questions

Concept explainers

Question

Suppose that Mairin has knit a collection of wool‑blend infinity scarves that she wants to sell in her Etsy shop for $28.00 each. However, she is worried that if the average price of comparable scarves is less than $28.00, hers would be less likely to sell.

Mairin selected a random sample of 9 similar hand‑knit, wool‑blend infinity scarves, and their prices are as follows.

$21.75,$24.00,$27.25,$29.95,$23.00,$26.00,$27.80,$33.50,$27.00$21.75,$24.00,$27.25,$29.95,$23.00,$26.00,$27.80,$33.50,$27.00

Use a left‑tailed one‑sample ?t‑test to determine whether the average price of hand‑knit, wool‑blend infinity scarves sold on Etsy is less than $28.00. Assume that the prices of all comparable scarves are normally distributed.

Mairin should (reject, accept, fail to accept) her null hypothesis. There is (sufficient, no, insufficient) evidence that the mean price of hand‑knit, wool‑blend infinity scarves is (greater than, different from, less than, equal two) $28.00.

**One-Sample t-Test Requirements and Hypothesis Selection**

When conducting a one-sample t-test, it is essential to ensure that certain requirements are met for the test to be valid. Consider the following options and select the most appropriate one:

1. **No**, Mairin selected a normally distributed random sample, but she does not know the population standard deviation.
2. **Yes**, Mairin selected a random sample that is normally distributed and contains no outliers.
3. **No**, Mairin selected a random sample from a normally distributed population, but her sample is too small.
4. **Yes**, Mairin selected a random sample from a normally distributed population, and her sample contains no outliers.

Next, you need to choose the appropriate null hypothesis ($H_0$) and alternative hypothesis ($H_1$) for the test.

**Hypotheses:**

- **$H_0$:**
- $\mu = 28.00$
- $\bar{x} = 26.69$
- $\mu = 26.69$
- $\bar{x} = 28.00$

- **$H_1$:**
- $\bar{x} = 26.69$
- $\mu < 26.69$
- $\bar{x} < 28.00$
- $\mu < 28.00$

**Calculation:**

Calculate the t-test statistic and round your answer to three decimal places. Enter your solution in the provided box:

$ t = \_\_\_\_\_\_\_\_\_ $

Use a *t*-distribution table to find a range of possible *P*-values for this test.

- ○ 0.15 < *P* < 0.20
- ○ 0.10 < *P* < 0.15
- ○ 0.05 < *P* < 0.10
- ● 0.20 < *P* < 0.25

Complete the conclusion of this test. Use a significance level of α = 0.10.

Mairin should [Dropdown] her null hypothesis. There is [Dropdown] evidence that the mean price of hand-knit, wool-blend infinity scarves is [Dropdown] $28.00.

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.

Expert Solution

Trending now

This is a popular solution!

Step by step

Solved in 2 steps with 20 images

SEE SOLUTION Check out a sample Q&A here

Knowledge Booster

$Conditional Probability, Decision Trees, and Bayes' Theorem$

Learn more about

Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, statistics and related others by exploring similar questions and additional content below.

Similar questions