Just like in Chapter 11, P is found in relation to z. The z score (or z test score as it is called in
chapter 14, since we’re looking at multiple samples rather than populations, as we were in
chapter 11, or single samples in chapter 3) gives us a point on the x axis of a Normal curve. The
table A gives us the proportion of the curve to the left of that point (a value from 0.001 to .9999)
which we can use to find the P value (more on that in 14.22). Z test statistics are calculated
Note that the portion of the equation in the brackets is itself an equation of division, where the
standard deviation of the population is divided by the square root of the number included in the
sample. See example 14.9 on page 379 of the textbook to see how this equation is used. This is
the equation we use for 14.40, where it gives us a value for z, which we then use to find the P
Since we are doing hypothesis testing, we use the P value to reject the null hypothesis. If the p
value is less than 0.05 (that is P<0.05) we can say that the data are statistically significant at the
5% level and reject the null hypothesis. If P<0.01, we can say that the data are statistically
significant at the 1% level and reject the null hypothesis.
If data are statistically significant, it means that the results did not occur ‘by chance’ and that it is
likely a good representation of the population beyond those sampled.
Significance from a table. A test of Ho: µ=1 against Ha: µ≠1 has test statistic z=1.776. Is this test
significant at the 5% level (α=0.05)? Is it significant at the 1% level?
Z* at the 5% level is 1.960. The given value 1.776 is smaller than this value. Since it fails to
meet the critical value, it is not significant at the 5% level. It necessarily is not significant at the
1% level (where the critical value is 2.576).
To determine significance by comparing P values, a two sided P is necessary because the Ha is
two sided (µ≠1). The z score is given, so table A (pg 691) can be used to look at the proportion
of the Normal curve being asked for. Z=1.77 (approximately, you could also use the value for
1.78 but the calculation will still be ‘off’ so to speak), the corresponding value is 0.9616. 1-
0.9616=0.0384. Because it is two sided, we need to multiply this value by two (to take into
account both extremes of the curve. Figure 14.7 and 14.8 are useful for illustrating this).
2x0.0384=0.0768. This value does not satisfy the critical values for a two sided P (0.05 and 0.01
respectively found for the two sided P in table C).
Student study times. Exercise 14.34 describes a class survey in which students claimed to
study an average of minutes on a typical weeknight. Regard these students as a SRS from the
population of all first-year students at this university. Does the study give good evidence that
students claim to study more than 2 hours per night on the average? (See 14.34 for the
standard deviation and the sample size)