Question

an article gave the following observations on maximum concrete pressure (kn/m2). 33.3 41.9 37.4 40.3 36.7 39.2 36.2 41.9 36.0 35.2 36.8 38.9 35.9 35.3 40.1 (a) is it plausible that this sample was selected from a normal population distribution? because of the number of observations, we ascertain that it is plausible that this sample was taken from a normal population distribution. because of the number of observations, we ascertain that it is not plausible that this sample was taken from a normal population distribution. using a normal probability plot, we ascertain that it is not plausible that this sample was taken from a normal population distribution. using a normal probability plot, we ascertain that it is plausible that this sample was taken from a normal population distribution. (b) calculate an upper confidence bound with confidence level 95% for the population standard deviation of maximum pressure. (round your answer to three decimal places.)

Answer 1

Normality assessment typically requires a normal probability plot, and normality cannot be asserted solely based on the number of observations. Calculating an upper confidence bound for the population standard deviation at a 95% confidence level requires the sample standard deviation and uses the Chi-squared distribution.

Step-by-step explanation:

The question provided involves the analysis of a sample data set to determine whether it is plausible that it was selected from a normally distributed population. One method to assess normality is by examining a normal probability plot. The plot compares the distribution of sample data to a perfect normal distribution. Without the plot provided, we cannot definitively say whether it is plausible or not. However, the number of observations alone (15 in this case) does not guarantee normality.

For calculating an upper confidence bound for the population standard deviation, we would typically use the Chi-squared distribution. Unfortunately, the sample standard deviation is not provided, which is necessary for this calculation. Should the sample standard deviation be known, the formula for the upper bound of the population standard deviation at 95% confidence level could be given as:

s\u00b2 \u00d7 (n-1)/X^2_{\u03b11-\u03b12,n-1}

where s\u00b2 is the sample variance, n is the sample size, and X^2_{\u03b11-\u03b12,n-1} is the Chi-squared value for \u03b11-\u03b12 confidence level and n-1 degrees of freedom.