State whether the following statements are True or False. -A fair coin is tossed

Question

State whether the following statements are True or False.

-A fair coin is tossed 6 times. The probability of it lands tails up exactly 3 times is 10× (1/2)^4 .

-A frequency distribution groups data into classes showing the number of observations in each class.

-If probability sampling is done, each item in the population has a chance of being chosen.

-A critical value is a Z-score separating unlikely value from those that are likely to occur.

-A point estimate is a single value or point used to approximate a population parameter.

-The number of women taller than 68 inches in a random sample of 5 women is an example of continuous random variable.

Explanation / Answer

State whether the following statements are True or False.

-A fair coin is tossed 6 times. The probability of it lands tails up exactly 3 times is 10× (1/2)^4 .

False

Explanation

We are given n = 6, p = probability of tail = 0.5 or (1/2) and X = 3

We have to find P(X=3)

P(X=x) = nCx*p^x*(1 – p)^(n – x)

P(X=3) = 6C3*(1/2)^3*(1/2)^3

P(X=3) = 20*(1/2)^6

P(X=3) = 0.3125

Required probability = 0.3125

-A frequency distribution groups data into classes showing the number of observations in each class.

True

Explanation

We know that the specific class of the frequency distribution showing the number of total items or observations in this class and this number is called as the frequency of this class.

-If probability sampling is done, each item in the population has a chance of being chosen.

True

Explanation

We know that there is same and equal chance of selection of each item in the population if probability sampling is done.

-A critical value is a Z-score separating unlikely value from those that are likely to occur.

False

Explanation

The critical value may be Z-score or t-score or any other value from several distributions which separates unlikely value form those that are likely to occur. It is not only Z-score value.

-A point estimate is a single value or point used to approximate a population parameter.

True

Explanation

In point estimation, we are dealing with the single value (Statistic) from the sample which is used to represent the population parameter.

-The number of women taller than 68 inches in a random sample of 5 women is an example of continuous random variable.

False

Explanation

The variable of interest is number of women taller than 68 inches. The variable number of women is a discrete random variable and number of women is described by integers and not a fraction.

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