Question

(1 pt) Katie thinks that people living in a rural environment have a healthier lifestyle than other people. She believes the average lifespan in the USA is 77 years. A random sample of 20 obituaries from newspapers from rural towns in Idaho give x = 77.69 and s = 1.92. Does this sample provide evidence that people living in rural Idaho communities live longer than 77 years? (a) State the null and alternative hypotheses: (Type "mu" for the symbol u, e.g. mu > 1 for the mean is greater than 1, mu< 1 for the mean is less than 1, mu not 1 for the mean is not equal to 1) ?? Ha (b) Find the test statistic, t- (c) Answer the question: Does this sample provide evidence that people living in rural Idaho communities live longer than 77 years? (Use a 10% level of significance) (Type: Yes or No)

Answer 1

Solution:-

5)

State the hypotheses. The first step is to state the null hypothesis and an alternative hypothesis.

Null hypothesis: P = 0.45
Alternative hypothesis: P ? 0.45

Note that these hypotheses constitute a two-tailed test. The null hypothesis will be rejected if the sample proportion is too big or if it is too small.

Formulate an analysis plan. For this analysis, the significance level is 0.05. The test method, shown in the next section, is a one-sample z-test.

Analyze sample data. Using sample data, we calculate the standard deviation (S.D) and compute the z-score test statistic (z).

S.D = sqrt[ P * ( 1 - P ) / n ]

S,.D = 0.05707
z = (p - P) / ?

z = - 1.43

where P is the hypothesized value of population proportion in the null hypothesis, p is the sample proportion, and n is the sample size.

Since we have a two-tailed test, the P-value is the probability that the z-score is less than -1.43 or greater than 1.43.

Thus, the P-value = 0.153

Interpret results. Since the P-value (0.153) is greater than the significance level (0.05), we cannot reject the null hypothesis.

From the above test we have sufficient evidence in the favor of the claim that early 45% of all Americans have brown eyes.