Table 1: Summary statistics of the extra sodium content (%) in the thirty samples Min. : 0.14 1st Qu.: 1.17 Median : 2.13 Mean : 2.4813 3rd Qu.: 3.86 Max. : 5.22 SD = 1.6156 Researchers believe that the average percentage of sodium content is 3%. Test the appropriate hypotheses using a 5% level of significance. Specify the following: random variable of interest parameter of interest (Symbol for the parameter) statistic you would use to estimate parameter
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.
Table 1: Summary statistics of the extra sodium content (%) in the thirty samples
| Min. : 0.14 1st Qu.: 1.17 Mean : 2.4813 3rd Qu.: 3.86 Max. : 5.22 SD = 1.6156 |
Researchers believe that the average percentage of sodium content is 3%. Test the appropriate hypotheses using a 5% level of significance.
- Specify the following:
- random variable of interest
- parameter of interest (Symbol for the parameter)
- statistic you would use to estimate parameter
The given part of this question is written on whiteboard:
We need to conduct a 5% hypothesis test to know whether the Researchers believe that the average percentage of sodium content is 3% is correct or not.
- the random variable of interest is “percentage of sodium content “
- Statistics of interest :
Sample mean percentage of sodium = 2.4813
Standard deviation = 1.6156
n = 30
Hypothesis Testing:
Calculations shown on whiteboard below:
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