A survey is being carried out by institute A to discover the average number (4) of inhabitants under 18 years of age per household in Brazil. In a random sample of 63 families across the country, it was found that 63 63 E1 ti = 183 and E x? = 639, where xi represents the number of inhabitants under 18 years of age in each household. Assume that the number of inhabitants under the age of 18 per household has a normal distribution. a) Determine the lower limit of the 99% confidence interval for the value of H. b) We want to find out the proportion (p) of households in the country with 3 or more inhabitants under 18 years of age. In the last survey carried out by institute A before the one mentioned in this question, it was found that this proportion was equal to 0.48. In the sample mentioned in this exercise, it was found that 56% of households have 3 or more inhabitants under 18 years of age. Perform a hypothesis test to check if there was an increase in the mentioned proportion, that is, test the null hypothesis H0 : p <= 0.48 against the alternative hypothesis H1:p > 0.48 Calculate the p-value of this test.
A survey is being carried out by institute A to discover the average number (4) of inhabitants under 18 years of age per household in Brazil. In a random sample of 63 families across the country, it was found that 63 63 E1 ti = 183 and E x? = 639, where xi represents the number of inhabitants under 18 years of age in each household. Assume that the number of inhabitants under the age of 18 per household has a normal distribution. a) Determine the lower limit of the 99% confidence interval for the value of H. b) We want to find out the proportion (p) of households in the country with 3 or more inhabitants under 18 years of age. In the last survey carried out by institute A before the one mentioned in this question, it was found that this proportion was equal to 0.48. In the sample mentioned in this exercise, it was found that 56% of households have 3 or more inhabitants under 18 years of age. Perform a hypothesis test to check if there was an increase in the mentioned proportion, that is, test the null hypothesis H0 : p <= 0.48 against the alternative hypothesis H1:p > 0.48 Calculate the p-value of this test.
MATLAB: An Introduction with Applications
6th Edition
ISBN:9781119256830
Author:Amos Gilat
Publisher:Amos Gilat
Chapter1: Starting With Matlab
Section: Chapter Questions
Problem 1P
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Transcribed Image Text:Note: All final answers must be rounded to 4 decimal places of approximation, but do not do any rounding
in the middle stages of the solution.
A survey is being carried out by institute A to discover the average number (H) of inhabitants under 18
years of age per household in Brazil. In a random sample of 63 families across the country, it was found
that
63
E1 x; = 183
Σ
and
639,
where xi represents the number of inhabitants under 18 years of age in each household. Assume that the
number of inhabitants under the age of 18 per household has a normal distribution.
a) Determine the lower limit of the 99% confidence interval for the value of H.
b) We want to find out the proportion (p) of households in the country with 3 or more inhabitants under 18
years of age. In the last survey carried out by institute A before the one mentioned in this question, it was
found that this proportion was equal to 0.48. In the sample mentioned in this exercise, it was found that
56% of households have 3 or more inhabitants under 18 years of age. Perform a hypothesis test to check if
there was an increase in the mentioned proportion, that is, test the null hypothesis
H0 :p <= 0.48 against the alternative hypothesis H1:p > 0.48. Calculate the p-value of this test.
C) Another independent survey carried out by institute B estimated that p = 0.56. After making the
calculations, it was found that if p = 0.56, then the probability of a type Il error occurring in the test
performed in the previous item is 0.33. What is the significance of the test performed in the previous item?
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