Question

Is the rate of hay fever lower for people over the age of 50 as compared to people under the age of 25? A random sample of ?1 = 16 communities in Western Kansas suggested that the sample mean rate of hay fever for people under age 25 (per 1000 population) was ?̅1 = 109.50with sample standard deviation ?1 = 15.41. A random sample of ?2 = 14 regions in Western Kansas suggested that the sample mean rate of hay fever for people over age 50 (per 1000 population) was ?̅2 = 99.36 with sample standard deviation ?2 = 11.57. Assume that the hay fever rate in each age group has an approximately normal distribution. Do the data indicate that the age group over 50 has a lower rate of have fever? Use ? = 0.05.

a) What is the level of significance? State the null and alternative hypotheses.

b) What sampling distribution will you use? Compute the sample test statistic and correspondingz or t value as appropriate.

c) Find or estimate the P-value.

d) Based on your answers in parts (a) through (c), will you reject or fail to reject the null hypothesis? Are the data statistically significant at level ??

e) Interpret your conclusion in the context of the problem.

Answer 1

Ans:

a)level of significance=0.05

b)We will use t-statistic.

pooled standard deviation=SQRT(((16-1)*15.41^2+(14-1)*11.57^2)/(16+14-2))=13.761

standard error=13.761*sqrt((1/16)+(1/14))=5.036

Test statistic:

t=(109.5-99.36)/5.036

t=2.014

c)df=16+14-2=28

p-value=tdist(2.014,28,1)=0.0269

d)As,p-value<0.05,we reject the null hypothesis.

Yes,data is statistically significant at level ?

e)There is sufficient evidence to conclude that  the age group over 50 has a lower rate of have fever.