In a random sample of 8 cell phones, the mean full retail price was $536.40 and the standard deviation was $183.00. Further research suggests that the population mean is $434.75. Does the t-value for the original sample fall between - to 99 and to 99? Assume that the population of full retail prices for cell phones is normally distributed. The t-value of t%D V fall between - to.99 and to 99 because to.99 =- (Round to two decimal places as needed.)
Inverse Normal Distribution
The method used for finding the corresponding z-critical value in a normal distribution using the known probability is said to be an inverse normal distribution. The inverse normal distribution is a continuous probability distribution with a family of two parameters.
Mean, Median, Mode
It is a descriptive summary of a data set. It can be defined by using some of the measures. The central tendencies do not provide information regarding individual data from the dataset. However, they give a summary of the data set. The central tendency or measure of central tendency is a central or typical value for a probability distribution.
Z-Scores
A z-score is a unit of measurement used in statistics to describe the position of a raw score in terms of its distance from the mean, measured with reference to standard deviation from the mean. Z-scores are useful in statistics because they allow comparison between two scores that belong to different normal distributions.
![### Statistical Analysis of Cell Phone Retail Prices
In a random sample of 8 cell phones, the following data was observed:
- **Mean Full Retail Price**: $536.40
- **Standard Deviation**: $183.00
Further research indicates that the population mean is $434.75. We need to determine if the t-value for the original sample falls between \(-t_{0.99}\) and \(t_{0.99}\), assuming that the population of full retail prices for cell phones is normally distributed.
#### Problem Statement:
Calculate the t-value and check if it falls within the specified range.
- **Formulation**: The t-value of t = [Box for Input] [Dropdown for +/- sign] fall between \(-t_{0.99}\) and \(t_{0.99}\) because \(t_{0.99} =\) [Box for Input].
#### Instructions:
1. **Round** all values to two decimal places as needed.
2. **Complete** the boxes with the appropriate calculations to solve the problem.
This task involves calculating the t-value using the sample mean, population mean, standard deviation, and sample size, then comparing it to the critical value \(t_{0.99}\) for hypothesis testing.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fa332979b-3709-48a2-942a-205e2ae2d053%2F7849a1e6-8d38-4e55-b9ff-c77b69389dbd%2Frcnyt4_processed.png&w=3840&q=75)
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