According to an NDP Group report, the mean number of meals prepared and eaten at home is 700 per year. Suppose that a random sample of 36 households showed a sample mean number of meals prepared and eaten at home was 690. Assume σ = 40. Test whether the population mean number of such meals is less than 700 using a significance level of 0.01. State the test statistic and p-value. Round your answers to four decimal places. Explain your conclusion to reject or fail to reject the null hypothesis in terms of p and α. Interpret your conclusion in the context of this problem.
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.
- According to an NDP Group report, the
mean number of meals prepared and eaten at home is 700 per year. Suppose that a random sample of 36 households showed a sample mean number of meals prepared and eaten at home was 690. Assume σ = 40. Test whether the population mean number of such meals is less than 700 using a significance level of 0.01. -
State the test statistic and p-value. Round your answers to four decimal places.
Explain your conclusion to reject or fail to reject the null hypothesis in terms of p and α. Interpret your conclusion in the context of this problem.
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