Question

22. Got a Minute? Students of one of the authors estimated the length of one minute withou réference to a watch or clock, and the times (seconds) are listed below. Use a 0.05 significance level to test the claim that these times are from a population with a mean equal to 60 seconds. Does it appear that students are reasonably good at estimating one minute? 69 81 39 65 42 21 60 63 66 48 64 70 96 91 65

Answer 1

(22)

H0:Null Hypothesis: $\mu$ = 60

HA: Alternative Hypothesis: $\mu \neq$ 60

From the given data, the following statistics are calculated:

n = 15

$\bar{x}$ = 940/15 = 62.6667

s = 19.4814

SE =s/$\sqrt{n}$

= 62.6667/$\sqrt{15}$ = 16.1805

Test statistic is:

t = (62.6667 - 60)/16.1805 = 0.1648

$\alpha$ = 0.05

ndf = n - 1 = 15 - 1 = 14

From Table, critical values of t = $\pm$ 2.1448

Since the calculated value of t = 0.1648 is less than critical value of t = 2.1448, the difference is not significant. Fail to reject null hypothesis.

Conclusion:

The data support the claim that these times are from population with a mean equal to 60 seconds.

(14)

H0:Null Hypothesis: $\mu$$\geq$ 3400

HA: Alternative Hypothesis: < 3400

n = 195

$\bar{x}$ = 3272.8

s = 660.2

SE =s/$\sqrt{n}$

= 660.2/$\sqrt{195}$ = 47.2779

Test statistic is:

t = (3272.8 - 3400)/47.2779= - 2.6905

$\alpha$ = 0.01

ndf = n - 1 = 195 - 1 = 194

From Table, critical values of t = - 2.3457

Since the calculated value of t = - 2.6905 is less than critical value of t = - 2.3457, the difference is significant. Reject null hypothesis.

Conclusion:

The data support the claim that the population of birth weights of males is less than 3600 g..