Question 1 true or false a If a random sample of size 12 has

Question 1: true or false:

a) If a random sample of size 12 has been drawn from a normal population, one can use t distribution to construct a 95% confidence interval for the population mean based on this sample.

b) Among a sample of 20 baseball players, 11 are left-handed. We hope to construct 95% confidence interval for the proportion of left-handed professional baseball players. Traditional method can be used for this purpose.

c) Standard error of the mean is the same with the sample standard deviation.

d) If the center of the target represents the parameter that we hope to estimate, which is an unbiased estimator?

(top left circle is a, top right is b, bottomm left is c, bottom right is d)

e) Two t distribution curves are drawn together in the figure below. The degree of freedom for curve (a) should be greater than the degree of freedom for curve (b).

(taller curve is a, shorter curve is b)

Solution

For the all question that I wil answer I will tell you why is false or true

a) If a random sample of size 12 has been drawn from a normal population, one can use t distribution to construct a 95% confidence interval for the population mean based on this sample.

true because we use Z distribution when n > 30

if n < 30 we can use t or Z distribution , it depends in if we know the standard deviation of population

b) Among a sample of 20 baseball players, 11 are left-handed. We hope to construct 95% confidence interval for the proportion of left-handed professional baseball players. Traditional method can be used for this purpose.

true , if traditional method you refer to Z distribution , so the answer is yes because we use z distribution for proportion in confidence intervals

c) Standard error of the mean is the same with the sample standard deviation.

TRUE

BECAUSE THE MEAN IS FROM SAMPLE, AND STANDARD ERROR IS FROM SAMPLE TOO

d) If the center of the target represents the parameter that we hope to estimate, which is an unbiased estimator?

AN UNBIASED ESTIMATOR IS WHEN THE PARAMETER IS THE SAME AS THE ESTIMATOR SO THE ANSWER IS A LETTER A) BECAUSE ALL THE POINTS ARE IN THE CENTER OF THE TARGET THAT IS THE PARAMETER

e) Two t distribution curves are drawn together in the figure below. The degree of freedom for curve (a) should be greater than the degree of freedom for curve (b).

df are the same as n-1

so when we have a greater value of n the curves will be more taller

so this is true