The sample mean foot length of a simple random sample of 25 third-graders is 22.5 cm. The standard error of the mean is 0.8 cm. Which one of the following is a correct interpretation for the standard error of the mean?

Question:

The sample mean foot length of a simple random sample of 25 third-graders is 22.5 cm. The standard error of the mean is 0.8 cm. Which one of the following is a correct interpretation for the standard error of the mean?

The typical distance between each individual foot length in the sample and the sample mean foot length is approximately 0.8 cm.

The typical distance between one sample mean foot length and another sample mean foot length is 0.8 cm.

The typical distance between each individual foot length in the population and the true mean foot length is approximately 0.8 cm.

The typical distance between means of samples of size 25 and the population mean foot length is approximately 0.8 cm

The typical distance between each individual foot length in the sample and the true mean foot length is approximately 0.8 cm.

The correct option is:

The typical distance between means of samples of size 25 and the population mean foot length is approximately 0.8 cm

Step-by-step explanation:

The standard error of the mean is a measure of the extent of variation of the mean in a sample of data from that of the value of the mean within the general population. It is a statistical measure of the probability that the size of a particular sample will approach that of the population mean, with reference to the principle of the central limit theorem.

Therefore, the interpretation of the standard error is that the variation between mean in a sample of 25 and that of the population is about 0.8 cm.

solution:

the given function is ,

      =

the three roots of this quadratic function is , 0 ,8 and 10.all the roots are real and rational.

if a quadratic equation is of the form ,

sum of the roots = a + b +c= 0+8+10=18=  

product of roots taken two at a time = a b + b c+ c a = 0+80+0=80 =  

product of roots = a b c = 0=  

there are 11 doors in a hall starting from 0 to 11.the entry in the hall is permitted through gate number 0 and exit is allowed through only gate number 8 and 10.so, three roots(0,8,10) of quadratic function is given by entry and exit route of this hall.