Athabasca fishing lodge is located on lake athabasca in northern Canada. In one
ID: 3293802 • Letter: A
Question
Athabasca fishing lodge is located on lake athabasca in northern Canada. In one of its recent brochures, the lodge advertises that 75% of its guests catch northern pike over 20 pounds. Suppose that last summer 64 out of a random sample of 83 guests did, in fact, catch northern pike weighing over 20 pounds.
Does this indicate that the population proportion of guests who catch pike over 20 pounds is different from 75% (either higher or lower)? Use
= 0.05.
What does the confidence interval tell you? Based on the values of the confidence interval, does your rejection decision make sense? Explain.
Explanation / Answer
If the p-value is less than or equal to the significance level , i.e., p-value , then we reject the null hypothesis and conclude the alternate hypothesis is true. If the p-value is greater than the significance level, i.e., p-value > , the significance level then we fail to reject the null hypothesis and conclude that the null is plausible. Note that we can conclude the alternate is true, but we cannot conclude the null is true, only that it is plausible.
The hypothesis test in this question is:
H0: p0 = 0.75 vs. H1: p0 0.75
The test statistic is:
z = ( 0.7710843 - 0.75 ) / ( ( 0.75 * (1 - 0.75 ) / 83 )
z = 0.443607
The p-value = P( Z > |z| )
= P( Z < -0.443607 ) + P( Z > 0.443607 )
= 2 * P( Z < -0.443607 )
= 0.6573268
Since the p-value is greater than the significance level of 0.05 we fail to reject the null hypothesis and conclude p = 0.75 is plausible.
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