Question

Is the temperature required to damage a computer on the average less than 110 degrees? Because of the price of testing, twenty computers were tested to see what minimum temperature will damage the computer. The damaging temperature averaged 109 degrees with a standard deviation of 3 degrees. Assume that the distribution of all computers' damaging temperatures is approximately normal. (6% significance)

Hypotheses:

Conditions:

Perform the test:

Results:

Decision

Conclusion

Answer 1

Solution:

1)

Hypotheses are

H₀ : $\mu$ = 110 vs H_a : $\mu$ < 110

2)

Sample is taken from a normal population.

Sample is random.

Population SD is unknown ,

So , we use t test

Use $\alpha$ = 6% = 0.06

3)

The test statistic t is

t =  
T-]/[s/n
= [109- 110]/[3 /$\sqrt{}$20] = -1.491

Now ,

d.f. = n - 1 = 20 - 1 = 19

One tailed left sided test

t = -1.491

$\alpha$ = 0.06

For left tailed test , critical value is

-ta,df -0.06.19 -1.628

Critical value is -1.628

Rejection region is < -1.628

4)

Results :

Test statistic t = -1.728

Critical value is -1.628

Rejection region is < -1.628

5)

Decision:

Reject the null hypothesis H₀ at 6% level of significance

6)

Conclusion:

There is sufficient evidence to support the claim that  the temperature required to damage a computer on the average is less than 110 degrees.