For this data set, an appropriate significance level is 0.05. This significance level is standard for most data sets that are of a large enough size, which would be considered a data set with more than 30 recorded responses, which is fulfilled by the above dataset.
Qualitative Variable: Food Type
Statistic: prop(Type,Burger)

For this variable, an appropriate sample size is 30. A sample of this size is considered large enough to calculate trusted and confident sample statistics for a variable. The confidence interval for this sample is as follows: 0.4649 ≤ ρ ≤ 0.6228. The margin of error for this resample is 0.0789. From the calculated confidence interval, it can be understood that for this sample, the true population parameter can be said to lie between 0.4649 and 0.6228 confidently with 95% confidence in this interval.
Based on the histogram displaying the distribution of sample means, one can interpret that the majority of the resampled statistics for this variable lie above sample mean. Additionally, the graph can be said to appear leftskewed.
Quantitative Variable 1: Saturated Fat
Statistic: mean(SaturatedFat)

For this variable, an appropriate sample size is 30. A sample of this size is considered large enough to calculate trusted and confident sample statistics for a variable. The confidence interval for this sample is as follows: 8.8684 ≤ µ ≤ 10.9108. The margin of error for this resample is 1.0167. From the calculated confidence interval, it can be understood that for this sample, the true population mean can be said to lie between 8.8684 and 10.9108 confidently with 95% confidence in this interval.
Based on the histogram displaying the distribution of sample means, one can interpret that the majority of the resampled statistics for this variable lie above sample mean. Additionally, the graph can be said to appear to follow a pattern that closely resembles a normal distribution.
From the calculated probability below, one can interpret that the probability of selecting another sample with the size of 30 and attaining a sample mean of at least 9.86985 is 0.56067, or has a 56.067% chance of occurring.
Quantitative Variable 2: TransFat
Statistic: prop(TransFat,0)

For this variable, an appropriate sample size is 30. A sample of this size is considered large enough to calculate trusted and confident sample statistics for a variable. The confidence interval for this sample is as follows: 0.3596 ≤ ρ ≤ 0.4825. The margin of error for this resample is 0.0614. From the calculated confidence interval, it can be understood that for this sample, the true population parameter can be said to lie between 0.3596 and 0.4825 confidently with 95% confidence in this interval.
Based on the histogram displaying the distribution of sample means, one can interpret that the majority of the resampled statistics for this variable lie above sample mean. Additionally, the graph can be said to appear rightskewed.
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Nov 27, 2017
For the second quantitative variable, we are interested in confidence interval for mean.