Question

1- Suppose a simple random sample of sizen is drawn froma large population with mean u and standard deviation o. The sampling distribution of x has mean ug and standard deviation= 2- As the number of degrees of freedom in the t-distribution increase, the spread of the distribution 3- True or False: The value of to.10 with 5 degrees of freedom is greater than the value of to.10 with 10 degrees of freedom. 4- True or False: To construct a confidence interval about the mean, the population from which the sample is drawn must be approximately normal. True or False: The distribution of sample mean, , will be normally distributed if the sample is obtained from the population that is not normal distributed, regardless of sample size. 5-

Answer 1

1. Sampling distribution of x:

Mean, µₓ = µ

Standard deviation, σₓ = σ/√n

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2. As the number of df in the t-distribution increases, the spread of the distribution becomes normal.

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3. True.

Critical value, t-crit = ABS(T.INV(0.10, 5)) = 1.476

Right tailed critical value, t-crit = ABS(T.INV(0.10, 10)) = 1.372

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4. False.

If the sample size is >= 30 or the population standard deviation is given, then we can find the confidence interval without knowing about the normality of the distribution.

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5. False.