Question

A national newspaper reported that the state with the ongest mee fe span is Ha ali where e popula on mean ife span is 79 years. A ra o m sample 0 20 obituary notices in e Hono u Ad er zer ฉave the fo o ing information about e span in years of Honolulu esidents 72 68 1 93 56 19 78 94 83 94 77 69 5 97 75 71 96 47 66 27 ф use a calculator with sample maan and standard deviation key to find x and (Round your answers to two decimal places.) yr i Assuming that life span n Honolulu appra imate y normally d strouted, does tns information inacate that the population mean li e span or Honolulu rescents s less than 79 years? use a 5% le e or signicance Whet is the level of significance? State the nul and aternate hypothases. b) What sampling distribution will you usa? Explain the rationala for your chaice of sampling distribution. O The Student's t, since we assume that x has a normal distrbution and ơ is unknown The Student's r. since vve assume that x nas normal distrbution and σ is known. O The standard normal, since we assume that x has a normal distribution and ơ is unknown. O The standard normal, since ile Rssume that x has a normal distribution and σ is knonn. What is the value of the sample test statistic? (Round your answer to three decimal places.) () Estimate the P-value. o P-value 0.2S0 0.100 Pvaluc0.250 O 0.050P-value 0.100 O 0.010 P-value0.050 value 0.010

Answer 1

i) Sample Mean, $\bar x = \Sigma x/n = 1428/20 = \textbf{71.4}$

Sample standard deviation, $s=\sqrt{(\Sigma(x_i-\bar x)^2)/(n-1)}$

$=\sqrt{\frac{(72-71.4)^2+(68-71.4)^2+...+(27-71.4)^2}{19}}$

$=\textbf{ 20.65}$

ii) a) Level of significance = 5% = 0.05

Null and alternative hypothesis:

$H_0:\mu=79\ ;\ H_1:\mu < 79$

b) Sampling distribution:

The Student's t, since we assume that x has a normal distribution and $\sigma$ is unknown.

Test statistic:

$t = \frac{\bar X - \mu_0}{s/\sqrt{n}} = \frac{ 71.4 - 79}{ 20.65/\sqrt{ 20}} = \textbf{-1.646}$

df = 20-1= 19

c) P-value = 0.058

0.050 < P-value < 0.100

Conclusion:

Fail to reject null hypothesis. There is not enough evidence to claim that the population mean is less than 79, at the 0.05 significance level