Question

(3) Daily caffeine beverage consumption for a sample of 8 adult American women in a stressful job has been given (in ounces) as 34.7, 35.4,34.7, 37.7, 32.5, 28,18.4, 24.9. The mean was thought to have been 29. Assuming a normal distribution, and assuming that this provides a representative sample, does the data suggest that 29 oz. is an appropriate assumption? Test the appropriate hypothesis using the 0.05 level of significance by following the steps outlined below.

- Describe specific Type I and Type II errors that could be made

Answer 1

We have to test for the population mean. We assume the data is normal and since the population SD is not given we use the t-test.

We have to test whether the assumption of 29 oz is correct or not. That is true mean different from 29 or not.

So this is a two tailed test.

	X	X2
1	34.7	1204.09
2	35.4	1253.16
3	34.7	1204.09
4	37.7	1421.29
5	32.5	1056.25
6	28	784
7	18.4	338.56
8	24.9	620.01
Total	246.3	7881.45

Mean =

SD =

  (The assumption is correct about the mean caffeine is 29 oz.)

  (The assumption is incorrect)

Test Stat =

null mean   

p - value = 2 P( > |Test Stat |) ........................using t-dist tables

Sample mean	30.7875
Sx	6.530027
n	8
Null mean	29
Test Stat	0.774241
p-value	0.466486
level of significance	0.05
since p-value > 0.05
Decision	Do not reject the null hypothesis at 5%.
Conclusion	There is insufficient evidence to conclude that the assumption is incorrect

- Describe specific Type I and Type II errors that could be made

Type 1 : To reject a true null hypothesis.

We conclude that the assumption is incorrect of 29 oz when in fact daily average caffeine consumption is 29 oz.

Type 2 : Fail to reject a false null hypothesis.

We conclude that the assumption is correct of 29 oz when in fact daily average caffeine consumption is not 29 oz.

Here since we are failing to reject the null hypothesis , there is a chance of making a type 2 error.