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# To find if there is significant difference in means using t-test

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According to the historical data, the life expectancy in the United States is equal to the life expectancy in the United Kingdom. A new study has been made to see whether this has changed. Records of individuals from the United States who died recently are selected at random. The individuals lived an average of years with a standard deviation of years. Records of individuals from the United Kingdom who died recently are selected at random and independently. The individuals lived an average of years with a standard deviation of years. Assume that the population standard deviation of the life expectancy can be estimated by the sample standard deviations, since the samples that are used to compute them are quite large. At the level of significance, is there enough evidence to support the claim that the life expectancy, , in the United States is not equal to the life expectancy, , in the United Kingdom anymore? Perform a two-tailed test. Then fill in the table below.
What's the null hypothesis?
What's the alternative hypothesis?
What type of test statistic? Choose one: ___Z ___ t ___ Chi Square ___F
What is the value of the test statistic (round to at least 3 decimal places)?
What is the p-value? (round to at least 3 decimal places)?
Can we support the claim that the life expectancy in the US is not equal to the life expectancy in the United Kingdom? YES or NO
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Amy has two ways to travel from her home in Norco to her office in Los Angeles. One is to go via the 10 Freeway, and the other is to go via 60 Freeway. In order to determine which way she should travel on a daily basis, Amy has recorded the travel times for samples of nine trips via the 10 Freeway and nine trips via the 60 Freeway. The following table gives the travel times (in minutes) for the eighteen trips:

Travel times in minutes
10 Freeway 75, 77, 76, 71, 68, 71, 67, 75, 72
60 Freeway 78, 66, 70, 73, 69, 72, 71, 75, 76

Assume that the two populations of travel times are normally distributed and that the population variances are equal. Can we conclude, at the level of significance, that the mean travel times of the two routes are different?
Perform a two-tailed test. Then fill in below:
What's the null hypothesis?
What's the alternative hypothesis?
What type of test statistic? Choose one: ___Z ___ t ___ Chi Square ___F
What is the value of the test statistic (round to at least 3 decimal places)?
What is the two critical values at the 0.01 level of significance? (round to at least 3 decimal places)?
Can we conclude that the mean travel times of the two routes are different? Yes or No
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