Question

End of Section Problem 9.22 According to data released by the World Bank, the mean PM10 (particulate matter) concentration for the city of Kabul, Afghanistan, in 1999 was 46. Suppose that because of efforts to improve air quality in Kabul, increases in modernization, and efforts to establish environmental-friendly businesses, city leaders believe rates of particulate matter in Kabul have decreased. To test this notion, they randomly sample 12 readings over a one-year period with the resulting readings shown below. Do these data present enough evidence to determine that PM10 readings are significantly less now in Kabul? Assume that particulate readings are normally distributed and that α = .01. 31 44 35 53 57 47 32 40 31 38 53 45

The value of the test statistic is t=___and we___(fail to reject the null hypoth. or reject the null hypoth.)

Answer 1

given mu = 46

n= sample size= 12

from the data mean , sample mean = 31+44+....+45 / 12 = AVERAGE(choose values)= 42.16667

sample standard deviation = s= SQRT(VAR.S(choose values)) = 9.123729

here we want to test the claim  to determine that PM10 readings are significantly less now in Kabul (ie., mu < 46)

So null hypothesis, H0 : mu = 46

against the alternative H1: mu < 46

since population standard deviation is unknown we use t test

test statistic = ( x bar - mu)/(s/square root(n))

t = (42.16667-46)/(9.123729/root (12))

t = -1.45544

Here degrees of freedom = n-1 =12-1 =11

at 11 degrees of freedom and 0.01 significance level , left tail test, critical value = -2.718

the decision is to reject H0 if t value > t critical value

here t value =-1.455 > -2.718 = critical value

so we fail to reject H0, at alpha = 0.01

So we conclude that we fail to reject H0, so there is not enough evidence to claim that M10 readings are significantly less now in Kabul.

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