Finding the P-values we gave in Examples 1 and 2 requires doing Normal distribution calculations using Table B of Normal percentiles. That was optional reading in Chapter 13 (pages 304–
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EXAMPLE 3 Tasting coffee
The hypotheses. In Example 1, we want to test the hypotheses
H0: p = 0.5
Ha: p > 0.5
Here, p is the proportion of the population of all coffee drinkers who prefer fresh coffee to instant coffee.
The sampling distribution. If the null hypothesis is true, so that p = 0.5, we saw in Example 1 that follows a Normal distribution with mean 0.5 and standard deviation, or standard error, 0.0707.
The data. A sample of 50 people found that 36 preferred fresh coffee. The sample proportion is .
The P-value. The alternative hypothesis is one-
Table B says that standard score 3.1 is the 99.9 percentile of a Normal distribution. That is, the area under a Normal curve to the left of 3.1 (in the standard scale) is 0.999. The area to the right is therefore 0.001, and that is our P-value.
The conclusion. The small P-value means that these data provide very strong evidence that a majority of the population prefers fresh coffee.
Test statistic
When conducting a statistical test of significance, the standard score that is computed based on the sample data is commonly referred to as a test statistic.
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NOW IT’S YOUR TURN
22.2 Coin tossing. Refer to Exercise 22.1 (page 528). We tossed a coin only 50 times and got 21 heads, so the proportion of heads is
This is less than one-
*This section is optional.