Question

6. For this step, please work under the assumption that we do not know the population mean and standard deviation (and in fact, if we are running this test, it means that we are not sure of these values). Construct a 95% confidence interval for the average height of a female. Interpret this confidence interval. HINT: You can use the “with data” option in StatCrunch to do this calculation.

7. It is a researcher’s belief that the average height of females has increased since the average value of 65 inches was reported. Using the sample of 30 female heights, conduct a hypothesis test at the .05 level that tests whether or not this researcher might be correct. You must state the null and alternative hypotheses as well as the p-value and an interpretation of what this means. HINT: You can use the “with data” option in StatCrunch to do this calculation.

8. How do the results from steps 6 and 7 relate to one another? HINT: does the true mean (given above these steps) lie in the interval found in step 6? How is this confirmed by the result in step 7

Height (in Inches)	Name
72.44	Emma
67.53	Olivia
66.71	Ava
62.02	Isabella
73.89	Sophia
65.95	Mia
65.83	Charlotte
64.15	Amelia
65.39	Evelyn
59.68	Abigail
64.24	Harper
66.60	Emily
65.40	Elizabeth
64.72	Avery
67.11	Sofia
61.97	Ella
62.83	Madison
67.20	Scarlett
66.62	Victoria
68.78	Aria
66.13	Grace
64.47	Chloe
66.64	Camila
62.39	Penelope
63.90	Riley
62.97	Layla
59.31	Lillian
66.14	Nora
67.54	Zoey
63.45	Mila

Answer 1

6)

calculate mean and standard deviation of the data given

sample mean 'x̄=	65.4
sample size   n=	30
sample std deviation s=	3.1125
std error 'sx=s/√n=	0.5683
for 95% CI; and 29 df, value of t=		2.045229642
margin of error E=t*std error    =		1.162226601
lower bound=sample mean-E =		64.2377734
Upper bound=sample mean+E =		66.5622266
from above 95% confidence interval for population mean =(64.2378,66.5622)

we are allowed to solve one question only.