Question

24 6 37 2) (Test the mean, o NOT given) The table below gives the number of floors at 18 randomly selected buildings in a city. Test the claim that the average number of floors in a building is less than 30. 45 30 14 4 36 55 12 26 17 18 14 35 40 12 6 Rejection Region H: H: TS: D: C: 3) (Test the P) A medical researcher claims that less than 25% of American adults are allergic to Penicillin. In of 800 adults, 20% say they have such an allergy. Test the researcher's claim at a = 0.05.

Answer 1

The number of floors at 18 randomly selected buildings in a city are :

45	30	24	12	6	37
14	4	14	26	18	40
36	55	35	17	12	6

Now, we have to test that the average number of floor in a building is less than 30.

HYPOTHESIS:

null hypothesis (H0) : $\mu$ = 30

alternative hypothesis (H1) : $\mu$ < 30

Since, population standard deviation ($\sigma$) is not given we estimate it by the sample standard deviation (s).

Here, the sample size is less than 30 and $\sigma$ is unknown so we use one sample t- test for testing the above hypothesis.

hull hypothesis (Ho): H=30 hypothesis (H1): " <36 Alternative Test statistie z T-M T Z Cocanned with CamScanner 5/6

N where, SE (standard erros 511 the sample mean 12 xi (5) Now, 2 23.94 M (under Hol 230 2 V Z (2:-x)" 14.86 cocanned With CamScanner ng 18

-6.06 Teal -- 1.7304 2 N1 23.94- 30 14.86 Vis 3.502 For the test - Statistic value the critical p-value will be 0-050871 Since, 0.050871 30-05 then, the result is not Statistically significant significant . So, we fail to reject the null hypothesis. Cocained with CamScanner

For, the given data we fail to reject the null hypothesis that the average number of floors in a building is 30 but not with a great deal of confidence. if we choose a slightly higher significance level , there might be a significant effect that is, the average number of floors might be less than 30, i.e, the caim might be true.