1400 is less
P = 0.10 n = 1400 np(1 – p) = 1400(0.10)(1 – 0.10) = 140(0.90) = 126 Since the sample size is less than 5% of the population and np(1‐p) = 126, which is greater than (or equal to) 10, that means the shape of the sampling distribution of p‐hat is approximately normal. The sample proportion is 154 / 1400 = 0.11 To decide if the 0.11 sample proportion is “unusual”, compute P(X> 126) = P(p‐hat > 0.11) because if a sample proportion of 0.11 is unusual, then any sample proportion greater than 0.11 is also unusual. To find the probability, which is the area to the right of p‐hat = 0.11 (to the right because it is GREATER than), convert p‐hat = 0.11 to a z‐score using the formula below, rounding to two 1400
z = .
.
.
= 1.25 Now find the area to the right of z = 1.25. .
.
= .
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= .
= 0.0080178373 Therefore the probability that the sample proportion is greater than 0.11, or P(X> 126) = P(p‐hat > 0.11) = 0.1056. This means that about 10.6 samples in 100 will result in a sample proportion of 0.11 or more. The is not necessarily evidence that the proportion of Americans who are afraid to fly has increased because typically an event with probability less than 0.05 (or 5%) is considered unusual (whereas the probability of this is 10.56% which is much larger than 5%).