A magazine reported that 47% of Canadians are confident they will take a winter vacation at some point between December through March. To test the magazine's claim, a random sample of 65 Canadians is taken and 27 of them said they are confident they will take a winter vacation at some point between December through March. At
A magazine reported that 47% of Canadians are confident they will take a winter vacation at some point between December through March. To test the magazine's claim, a random sample of 65 Canadians is taken and 27 of them said they are confident they will take a winter vacation at some point between December through March. At 5% significance level do the sample data provide sufficient evidence to support that the actual percentage is smaller than what the magazine reported?
A. What are the null and alternative hypotheses?
(Type "mu" for the symbol μ, "xbar" for the symbol x¯, "p" for the symbol p, or "phat" for the symbol ?̂ p^, e.g. mu > 0.5 for the mean is greater than 0.5, xbar < 0.5 for the sample mean is less than 0.5, p not = 0.5 for the proportion is not equal to 0.5, phat = 0.5 for the sample proportion is equal to 0.5.
Percentages should be provided as values between 0 and 1. Please do not include units.)
H0 =
Ha =
B. What is the test statistic value? (Include as many decimals as possible.)
Test statistic.
C. What is the associated p-value? (Include as many decimals as possible.)
p-value
D. Statistical decision:
A. There is evidence to support the alternative hypothesis at the 5% significance level and we would therefore accept the alternative hypothesis.
B. There is evidence to support the alternative hypothesis at the 5% significance level and we would therefore reject the null hypothesis.
C. There is not enough evidence to support the alternative hypothesis at the 5% significance level and we would therefore fail to reject the null hypothesis.
D. There is not enough evidence to support the alternative hypothesis at the 5% significance level and we would therefore accept the null hypothesis.
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