Would cause neither statement to be true b h 0 100 vs

would cause neither statement to be true.
b) H
0
: = 100 vs. H x̄
a
: < 100 or could write as H x̄
0
: >= 100 vs. H x̄
a
: < 100
The hypothesis needs to address the parameter not the statistic
c) H
0
: p ^ = 0.50 vs. H
a
: p ^ ≠ 0.50
The hypothesis statements should address population parameter (p) not sample statistic
(p^)
x̄
3. Patient satisfaction. Scores derived from a patient satisfaction survey are Normally distributed
with μ = 50 and σ = 7.5, with high scores indicating high satisfaction. An SRS of n = 36 is taken
from this population.
a) What is the standard error (SE) of x for these data?
b) We seek to discover if a particular group of patients comes from this population in which
μ = 50. Sketch the curve that describes the sampling distribution of the sample mean
under the null hypothesis. Mark the horizontal axis with values that are ±1, ±2, and ±3
standard errors above and below the mean.

3
c. Suppose in a sample of n = 36 from this particular group of patients the mean value
of x is 48.8. Mark this finding on the horizontal axis of your sketch. Then compute a
z statistic for this scenario and make sure it matches your sketch.
47.5 48.75 48.8 50 51.25 52.5
d. What is the two-sided alternative hypothesis for this scenario? e. Find the corresponding p-value for your z-statistic using Table B. f. Draw a conclusion for this study scenario based on your results.
Problems retrieved from Gerstman, B. B. (2015). Basic biostatistics: Statistics for public health practice (2nd ed.). Burlington, MA:
Jones and Bartlett. ISBN: 978-1-284-03601-5