Question

# True or false: 1. When constructing a confidence interval for a sample Mean, the t distribution...

True or false:
1. When constructing a confidence interval for a sample Mean, the t distribution is appropriate whenever the sample size is small.

2. The sampling distribution of X (X-bar) is not always a normal distribution.

3. The reason sample variance has a divisor of n-1 rather than n is that it makes the sample standard deviation an unbiased estimate of the population standard deviation.

4. The error term is the difference between the actual value of the dependent variable and the corresponding mean value of the dependent variable.

5. The Coefficient of Determination shows the direction of relationship between the dependent and the independent variables.

6. Assuming the same level of significanceα, as the sample size increases, the value of tα/2 (t- half alpha) becomes larger and larger than the value of zα/2(Z-half alpha).

7. When the level of confidence and the sample size remain the same, a confidence interval for a population mean µ will be narrower, when the sample standard deviation s is smaller than when s is larger.

Ans:

1)False,when population standard deviation is known and is normal,we can use z interval even for smaller sample sizes.

2)True,when population is not normally distributed or sample size is small.

3)True

4)False,error is difference between observed and predicted value of dependent variable.

5)False,direction is measured by coefficient of correlation.

6)False,as the sample size increases,t value becomes smaller and approaches toward the value of z.

7)True,smaller the standard deviation,smaller the margin of error,hence narrower the confidence interval.