A simple random sample of 10 subjects finds that the sample mean is 56 and the standard deviation is 4. Find the 98% confidence interval for u. Display the result in interval notation. You must round your result to decimal places. Remember that the information you have is from a small sample, you must use the t distribution. Remember that critical values ​​can be calculated in EXCEL using the degrees of freedom (n-1) and the level of significance (I - C) as a function of T.INV 2T (Level of Significance, Degrees of Freedom) Select one: a. The interval is: (53,057, 58,943) b. The range is: (53,521, 58,479). c. The interval is: (51,080, 60,920) d. The interval is: (51.991, 60.009) e. The interval is: (52,431, 59,569)

The distribution of scores on a standardized test is approximately Normal with standard deviation of σσ = 22. If a sample of 150 students had a mean score of x¯x¯ = 74.3, use this to find a 99% confidence interval for the mean score of all students on this test. We are 99% confident that the the mean score of students on this test was in the interval     What is the margin of error for your confidence interval? Margin of error =

In 1940 the average size of a U.S. farm was 174 acres. Let's say that the standard deviation was 51 acres. Suppose we randomly survey 45 farmers from 1940. I need help with the question below: The middle 50% of the distribution for x̅, the bounds of which form the distance represented by the IQR, lies between what two values? please explain to me the steps I have to do to solve this problem, thank you

The Z-score tells you the number of standard deviations away from the mean (and in what direction) a data value is. The formula: Z = *- can be used to find the Z-score for a single member of the population. Notice X - μ tells you the signed distance the data value (X) is from the mean. When you divide that by the size of each chunk (the standard deviation) you are measuring the distance in units of the size of the standard deviations (how many standard deviations fit in the distance between the data value and the mean) - which gives you the Z-score. The formula X = μ+Z.o can be used to find the value in the population when given the Z-score (signed number of standard deviations). Notice that Z. tells you how far from the mean the data value is (since Z is the number of standard deviations and is the size of each standard deviation the product tells the total distance). So adding the distance from the mean to the mean gives the location along the number line for the data value. A…