Question

The nine items of a sample had the following values

45, 47, 50, 52, 48, 47, 49, 53, 51
Does the mean of nine items differ significantly from an assumed normal population mean of 47.5 at 0.05 level of significance.​

Answer 1

Answer:

The mean of above values is 49.11. The answer is different from the assumed mean which is 47.5.

Step-by-step explanation:

You can not assume the answer. you have to calculate the answer form the given below formula.

Mean is the ratio of sum of all the observations to the total no. of observations.

                               ⇒  Mean =

                                ⇒   m =  

                                ⇒   m =

                                ⇒   m = 49.11

This is the required mean, assumption is wrong which is 47.5.

we can also find median. as, median is the middle most value of all the observations, if these observations are arranged in accendign order.

Answer 2

Given:

Nine items of a sample - 45, 47, 50, 52, 48, 47, 49, 53, 51

To Find:

Mean Of the Nine items and whether it differs from the assumed population mean.

Solution:

• The formula for Mean = {Sum of Observation} ÷ {Total numbers of Observations}.
• The above formula has to be used in order to find the Mean of the Nine items.

• The Assumed Mean of the normal population is 47.5.

∴ By applying the formula, we get:

Mean = {Sum of Observation} ÷ {Total numbers of Observations}

= 45 + 47 + 50 + 52 + 48 + 47 + 49 + 53 + 51 ÷ 9

= 442 ÷ 9

= 49.11

• The Mean value of the Nine items differ from the assumed normal population Mean.

∴ The difference stands at:

Mean - Assumed normal population Mean

= 49.11 - 47.5

= 1.61.

Thus, Both the Mean differ significantly by 1.61.