Question

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Back in the 1970s it was estimated that about 10% of Americans hunt. However, many of those close to the hunting sport believe there is a decline in the percentage of those that hunt now. A recent study by the US Fish and Wildlife Services found that of the 846 Americans surveyed, 53 of them say they hunt. Using a significance level of 0.05, test the claim that the proportion of American hunters now is less than what it was in the 1970s. b. Calculate the test statistic (round p-hat to two decimal places and round your answer to two decimal places.)

Answer 1

b)

The following information is provided: The sample size is N = 846, the number of favorable cases is X 53, and the sample proportion is p = X 0.0626, and the significance level is a = 0.05 53 846 (1) Null and Alternative Hypotheses The following null and alternative hypotheses need to be tested: Ho:p=0.10 Ha:p < 0.10 This corresponds to a left-tailed test, for which a z-test for one population proportion needs to be used. (2) Rejection Region Based on the information provided, the significance level is a = 0.05, and the critical value for a left-tailed test is ze = -1.64. The rejection region for this left-tailed test is R= {z:z < -1.64} (3) Test Statistics The Z-statistic is computed as follows: 2 = p - po V Po(1 – po)/n 0.0626 – 0.10 10.10(1 – 0.10)/846 -3.621

c)

P( X ≤ -2.11 ) = 0.0174292

this calculated p-value is less than given significance level 0.05, so we reject null hypothesis.it means there is sufficient evidence to claim that there is a decline in percentage.

R code should be:

pnorm(q=-2.11, mean=0, sd=1, lower.tail=TRUE, log.p = FALSE)

dnorm (x=-2.11, mean=0, sd=1)

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