The average life span in Ontario in 2009 was 81.3 years. A random sample of 17 obituaries from newspapers in Ontario sho

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The average life span in Ontario in 2009 was 81.3 years. A
random sample of 17 obituaries from newspapers in Ontario showed 𝑥¯
= 82.5 and 𝑠 = 2.6. If lifespan is assumed to be normally
distributed, does this sample provide sufficient evidence to
support that the average lifespan in Ontario has increased at the
1% significance level. 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 𝑝̂ , 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 not enough evidence to support the alternative
hypothesis at the 5% significance level and we would therefore fail
to reject the null hypothesis.
B. There is not enough evidence to support the alternative
hypothesis at the 1% significance level and we would therefore
reject the alernative hypothesis.
C. There is evidence to support the alternative hypothesis at
the 1% significance level and we would therefore reject the null
hypothesis.
D. There is not enough evidence to support the alternative
hypothesis at the 1% significance level and we would therefore fail
to reject the null hypothesis.
E. There is evidence to support the alternative hypothesis at
the 1% significance level and we would therefore accept the null
hypothesis.