Dwight wants to estimate the mean calorie content in beets with 90% confidence. He believes that the true population standard deviation of calorie content is 17 calories. What is the smallest number of beets that Dwight must sample so that the estimate is within 2 calories of the true mean? It takes 3 minutes per beet to gather and record the sample data. If Dwight has a total of 480 minutes (8 hours) available to collect the data, does he have enough time to collect a sample of this size?
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.
Dwight wants to estimate the mean calorie content in beets with 90% confidence. He believes that the true population standard deviation of calorie content is 17 calories. What is the smallest number of beets that Dwight must sample so that the estimate is within 2 calories of the true mean?
It takes 3 minutes per beet to gather and record the sample data. If Dwight has a total of 480 minutes (8 hours) available to collect the data, does he have enough time to collect a sample of this size?
The population standard deviation, sigma is 17.
The z-critical value for the 90% confidence interval is 1.645 which can be obtained by using the excel formula “=NORM.S.INV(0.95)”.
The margin of error, E is 2.
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