Question

According to the historical data, the life expectancy in the United States is less than or equal to the life expectancy in Ireland. A new study has been made to see whether this has changed. Records of 290 individuals from the United States who died recently are selected at random. The 290 individuals lived an average of 77.8 years with a standard deviation of 7.8 years. Records of 205 individuals from Ireland who died recently are selected at random and independently. The 205 individuals lived an average of 76.1 years with a standard deviation of 6.1 years. Assume that the population standard deviations of the life expectancies can be estimated by the sample standard deviations, since the samples that are used to compute them are quite large. At the 0.01 level of significance, is there enough evidence to support the claim that the life expectancy, y, in the United States is greater than the life expectancy, uz, in Ireland? Perform a one-tailed test. Then fill in the table below. Carry your intermediate computations to at least three decimal places and round your answers as specified in the table. The null hypothesis: ť s The alternative hypothesis: * ] ! % XIF no os o The type of test statistic: (Choose one)" Gooo 020 0-0 00 00 x 6 ? wol The value of the test statistic: (Round to at least three decimal places.) The p-value: (Round to at least three decimal places.) Can we support the claim that the life expectancy in the United States is greater than the life expectancy in Ireland? Yes No

Please answer neatly and correctly!

Answer 1

From the given information:
n1 = 290, n2 = 205
X1 = 77.8
s1 = 7.8
X2 = 76.1
s2 = 6.1

Null Hypothesis: u1 <= u2
Alternate Hypothesis: u1 > u2

We will be performing a two sample independent t-test (one-tailed)
Type of test statistic = t

The formula is:

(n-1) (n2-1)s% --2 n4+n2-2

First, let's calculate pooled standard deviation:

Sp² = 51.0621

t = (77.8 - 76.1)/0.652 = 1.7/0.652 = 2.6074

df = n1 + n2 - 2 = 493

At df = 493, the p-value = 0.0047 (from the t-table)

As the p-value < 0.05, we reject the null hypothesis. Hence, we can support the said claim. Correct option: Yes