A magazine reported that 47% of Canadians are confident they will take a winter vacation at some point between December
Posted: Fri Dec 24, 2021 10:16 am
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 𝜇μ, "xbar" for the symbol 𝑥¯x¯,
"p" for the symbol 𝑝p, or "phat" for the
symbol 𝑝̂ 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.)
𝐻0H0 :
𝐻𝑎Ha :
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 not enough evidence to support
the alternative hypothesis at the 5% significance level and we
would therefore accept the null 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 evidence to support the
alternative hypothesis at the 5% significance level and we would
therefore accept the alternative hypothesis.
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 𝜇μ, "xbar" for the symbol 𝑥¯x¯,
"p" for the symbol 𝑝p, or "phat" for the
symbol 𝑝̂ 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.)
𝐻0H0 :
𝐻𝑎Ha :
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 not enough evidence to support
the alternative hypothesis at the 5% significance level and we
would therefore accept the null 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 evidence to support the
alternative hypothesis at the 5% significance level and we would
therefore accept the alternative hypothesis.