Let X be the time (in minutes) required for the body temperature of a desert liz

Question

Let X be the time (in minutes) required for the body temperature of a desert lizard to reach 45C, starting from its normal body temperature while in the shade. The time in minutes observed for the body temperature of a desert lizard to reach 45C are the following: 10.1; 12.5; 12.2; 10.2; 12.8; 12.1; 11.2; 11.4; 10.7; 14.9; 13.9; 13.3 Assume data from this study is normally distributed, standard deviation = 1.07 or variability = 1.1449. Can it be concluded that the standard deviation of random variable X which is the time it takes to reach the lethal dose is less than 1.07 minutes?

(a) Using statistical notation establish the null and alternative hypotheses

(b) Compute the appropriate test statistic

(c) Report the critical value with the corresponding degrees of freedom

(d) Establish a conclusion in context of the problem

(e) Construct and interpret a 95% confidence interval for the population variance ^2

Explanation / Answer

(A) H0  : < 1.07

Ha : 1.07

where is the standard deviation of time it takes to reach the lethal dose.

(b) Here sample standard deviation s = 1.4786

Here test statistic

X2 = (n-1) (s/0)2 = (12 - 1) * (1.4786/1.07)2 = 21.01

(c) here dF = 12 -1 = 11 and alpha = 0.05

critical test statistic X2critical = 19.675

so as here X2 > X2critical   we can reject the null hypothesis and say that  standard deviation of time it takes to reach the lethal dose is not less than 1.07 minutes.

(e) Here 95% confidence interval for population variance 2

Here lower limit = (n-1) s2/X20.025 = (12 - 1) * 1.1449/ 21.92 = 0.5745

Upper limit = (n-1) s2/X20.975  = (12 -1) * 1.1449/3.8157 = 3.300

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