Question

Use the data set shown in the table below for this question. The data set contains a sample showing the payments of a random sample of bill payments and the values are in dollars. Assume that the payments are normally distributed. There are 14 observations. Be sure to copy/use all of them during your analysis.

a) The point estimate for the mean payment is [ Select ] .

b) The sample standard deviation is.

c) The probability of drawing a payment greater than $200 is [ Select ] .

d) The probability of drawing a payment less than $120 is is 0.2282 .

Suppose that the population standard deviation is the same as the sample standard deviation. Also, suppose that the population mean is the same as the sample mean.

e) For a sample of 20 observations the standard error is [ Select ] .

f) For a sample of 20, the probability of getting a sample mean of less than $140 is [ Select ] .

g) For a sample of 20, the probability of getting a sample mean of greater than $160 is [ Select ] .

h) For a sample of 20, the probability of getting a sample mean between $145 and $155 is [ Select ] .

Spend 191 226 55 208 166 167 166 159 159 127 81 201 138 128

Answer 1

Answering only first two parts

1)

Step 1: Calculate the mean of the 14 sample values

Answer: 155.15 = $\overline{x}$

Point Estimate is the square of sample variance given by the following formula:

$s^{2} = \sum (x - \overline{x})^{^{2}}/ n-1$

Calculating numerator of the above formula with each value given

$\sum (x - \overline{x})^{^{2}}$=28957.71

Since N=14, therefore,

$s^{^{2}}$ = 2227.516

2)

Square root of $s^{^{2}}$ is the sample standard deviation = 47.19657