Rhys is a quality control manager at a facility that manufactures snack foods. He is interested in the number of whole mini-pretzels that are in the 10 oz bags in the latest lot produced. Rhys selects 24 bags of mini-pretzels at random from the latest lot and counts the number of pretzels in each bag. The results of Rhys's sample are provided in the table below.
159 | 157 | 160 | 158 | 156 | 160 | 159 | 161
157 | 160 | 157 | 158 | 156 | 159 | 156 | 155
157 | 158 | 159 | 157 | 158 | 156 | 158 | 160
Of 1,000 rerandomizations of the data values in the sample, 2.5% of the resulting sample means are less than 157.33, 5% are less than 157.42, 10% are less than 157.54, 50% are less than 157.98, 90% are less than 158.33, 95% are less than 158.46, and 97.5% are less than 158.54.
What is a reasonable estimate for the margin of error that you would expect to contain the means for about 90% of all rerandomizations for these 24 values?
A) 157.54 to 158.33 <--- my answer
B) 157.33 to 158.54
C) 157.42 to 158.46
D) 0 to 158.33
I dont understand this at all and feel like my answer is wrong. Can someone please explain how to properly solve this
To solve this question, we need to understand the concept of margin of error. The margin of error is a measure of the uncertainty associated with a sample statistic, such as the mean. It provides a range within which the true population parameter is likely to fall.
In this case, Rhys sampled 24 bags of mini-pretzels and recorded the number of pretzels in each bag. We are interested in estimating the mean number of pretzels for the entire population of 10 oz bags in the latest lot. To estimate the margin of error, we can use the information provided about the rerandomizations of the data values in the sample.
The given information states that, for 90% of the rerandomizations, the resulting sample means are less than 158.33. This means that 90% of the time, the sample mean falls below 158.33. Therefore, we can infer that the margin of error, which represents the distance from the sample mean to the true population mean, would fall within the range of 157.33 to 158.33.
So, based on the information provided, the correct answer is B) 157.33 to 158.54.