Question

The null and alternative hypotheses for a problem are: H0: p ≤ 0.40 Ha: p > 0.40 The sample information for the problem is: n = 150 X = 74 (Count of the number of successes) How do you know that the sample mean of this problem (P with bar on top) is normally distributed?

a. Since 74 ≥ 5 and 76 ≥ 5 we know that P with bar on top is normally distributed. b. Since 60 ≥ 5 and 90 ≥ 5 we know that P with bar on top is normally distributed. c. Since 150 ≥ 30 we can rely on the Central Limit Theorem to know that P with bar on top is normally distributed. d. We must assume the population is normally distributed.

Answer 1

The given information is:

*The hypothesis is,

*The sample size (n) is 150.

*The number of successes (x) is 74.

If the size of the chosen sample (n) is large and the below stated conditions are satisfied,

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then the sampling distribution of proportion follows normal distribution with mean (p) and standard deviation .

So,

Since np = 60 and n(1 – p) = 90 are greater than 5, so it can be said that the conditions are satisfied.

Therefore, the correct statement is “Since 60 ≥ 5 and 90 ≥ 5 we know that P with bar on top is normally distributed”.

Hence, the option (b) is correct.