Question

please help with all parts and show work

7 6) A survey was done to determine if the Cholesterol level of Americans was different than that of Canadians. Sampling from both the US and Canada yielded the following results. Sample Size Mean Cholesterol Sample Standard Deviation 7.7 7.2 US Canada 44 38 179.6 175.8 Is there enough evidence at the 5% significance level to say that the cholesterol levels of US citizens and Canadian citizens differ? YES NO Please show the four steps of your analysis in the space provided below...

Answer 1

The cholesterol level of U.S. citizens and canadian citizens are given below

X is cholesterol level for U.S. citizens

Y is  cholesterol level for canadian citizens

	Sample Size	Mean	StDev
U.S.	44	179.6	7.7
Canada	38	175.8	7.2

Hypothesis

Null Hypothesis: There is no signifianct differrence between cholesterol level among American and Canandian citizens .

Alternate Hypothesis: There is signifianct differrence between cholesterol level among American and Canandian citizens.

Test Statistics:

X-Y T 179.6 – 175.8 7.473/ #2 + = 2.30 Sp Image 1 ni 1 38 n2

where n₁ and n₂ are the sample sizes,
X
and $\bar{Y}$ are the sample means, and
Is
and
S.
are the sample variances.

and

2 (ni – 1)sí + (n2 - 1)s ni + n2 - 2 = 55.8483 P

Reject the null hypothesis that the two means are equal if

• |T| > t_1-α/2,ν

where t_1-α/2,ν is the critical value of the t distribution with ν degrees of freedom If equal variances are assumed, then

V = n1 + n2 – 2 = 44 +38 - 2 = 80

The absolute value of the test statistic for our example, 2.30, is greater than the critical value of 1.99, and also P-value=0.02428 is less than level of significance 0.05 so we reject the null hypothesis and conclude that the two population means are different at the 0.05 significance level.

Conclusion :There is enough evidence at 5% level of significance to say that the cholesterol level of U.S. Citizens and Canandian citizens differ significantly.