Hypothesis test for the difference of population mean: Z test According to the historical data, the life expectancy in Belgium is less than or equal to the life expectancy in the United States. A new study has been made tosee whether this has changed. Records of 270 individuals from Belgium who died recently are selected at random. The 270 individuals lived an average of 78.3years with a standard deviation of 7.0 years. Records of 235 individuals from the United States who died recently are selected at random and independently. The235 individuals lived an average of 76.6 years with a standard deviation of 6.5 years. Assume that the population standard deviations of the life expectanciescan be estimated by the sample standard deviations, since the samples that are used to compute them are quite large. At the 0.05 level of significance, is thereenough evidence to support the claim that the life expectancy, 4, in Belgium is greater than the life expectancy, l,, in the United States? Perform a one-tailedtest. 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. (If necessary, consult a list of formulas.)pThe null hypothesis:H, :0The alternative hypothesis:H :0O=0OSOThe type of test statistic:(Choose one) vThe value of the test statistic:(Round to at least threedecimal places.)The critical value at the 0.05level of significance:(Round to at least threedecimal places.)Can we support the claim that the life expectancyin Belgium is greater than the life expectancy in theUnited States?YesO No

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Description: Hypothesis test for the difference of population mean: Z test According to the historical data, the life expectancy in Belgium is less than or equal to the life expectancy in the United States. A new study has been made tosee whether this has changed

For Belgium, sample size n1 = 270, sample mean = 78.3 and sample SD = 7.0 For United States, sample…

Answered: The null hypothesis: H, :0 The…

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Hypothesis test for the difference of population mean: Z test

According to the historical data, the life expectancy in Belgium is less than or equal to the life expectancy in the United States. A new study has been made to
see whether this has changed. Records of 270 individuals from Belgium who died recently are selected at random. The 270 individuals lived an average of 78.3
years with a standard deviation of 7.0 years. Records of 235 individuals from the United States who died recently are selected at random and independently. The
235 individuals lived an average of 76.6 years with a standard deviation of 6.5 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 0.05 level of significance, is there
enough evidence to support the claim that the life expectancy, 4, in Belgium is greater than the life expectancy, l,, in the United States? 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. (If necessary, consult a list of formulas.)
p
The null hypothesis:
H, :0
The alternative hypothesis:
H :0
O=0
OSO
The type of test statistic:
(Choose one) v
The value of the test statistic:
(Round to at least three
decimal places.)
The critical value at the 0.05
level of significance:
(Round to at least three
decimal places.)
Can we support the claim that the life expectancy
in Belgium is greater than the life expectancy in the
United States?
Yes
O No

Definition Definition Measure of central tendency that is the average of a given data set. The mean value is evaluated as the quotient of the sum of all observations by the sample size. The mean, in contrast to a median, is affected by extreme values. Very large or very small values can distract the mean from the center of the data. Arithmetic mean: The most common type of mean is the arithmetic mean. It is evaluated using the formula: μ = 1 N ∑ i = 1 N x i Other types of means are the geometric mean, logarithmic mean, and harmonic mean. Geometric mean: The nth root of the product of n observations from a data set is defined as the geometric mean of the set: G = x 1 x 2 ... x n n Logarithmic mean: The difference of the natural logarithms of the two numbers, divided by the difference between the numbers is the logarithmic mean of the two numbers. The logarithmic mean is used particularly in heat transfer and mass transfer. ln x 2 − ln x 1 x 2 − x 1 Harmonic mean: The inverse of the arithmetic mean of the inverses of all the numbers in a data set is the harmonic mean of the data. 1 1 x 1 + 1 x 2 + ...

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