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Name: ___________________________________
AP Statistics
Hypothesis Testing WS #1
1) For the following pairs, indicate which aren’t legitimate hypotheses and explain why.
a) H0:p  .4: Ha: p > .4
b) H0: x = 16: Ha: x > 16
H0: p = 4 Null hypothesis is always about
what p (or  ) =.
Hypothesis are always about parameters (population mean or
proportion), never statistics (sample mean or proportion). Will
always be
  , never x  (for a mean).
c) H0:  = 24: Ha:  > 24
These are legitimate hypotheses.
2) For each situation, state the null and alternative hypothesis.
a) Researchers have postulated that, due to differences in diet, Japanese children have a lower mean blood
cholesterol level than U.S. children. Suppose that the mean level of U.S. children is known to be 170.
H0:   170 Null Hypothesis: the mean blood cholesterol level of Japanese children = that of U.S. children
Ha :
  170
Alternative Hypothesis: the mean blood chol. level of Japanese children is less than that of U.S.
children.
b) A water quality control board reports that water is unsafe for drinking if the mean nitrate concentration
exceeds 30 ppm. Water specimens are taken from a well.
H0:   30 Null Hypothesis: the mean nitrate concentration of water if 30 ppm.
Ha :
  30
Alternative hypothesis: the mean nitrate concentration of water exceeds 30 ppm.
c) Last year, your company ‘s service technicians took an average of 2.6 hours to respond to trouble calls from
business customers who had purchased service contracts. Do this year’s data show a different average
response time?
H0:   2.6 Null Hypothesis: the average response time for service techs. this year is 2.6 hours.
Ha :
  2.6
Alternative Hypothesis: the average response time for service techs this year is not 2.6 hours.
d) Census Bureau data show that the mean household income in the area served by a shopping mall is $42,500
per year. A market research firm questions shopper at the mall. The researchers suspect that mean household
income of mall shoppers is higher than that of the general population.
H0:   42,500 Null Hypothesis: mean household income of mall shoppers is $42,500/year
Ha :
  42,500
Alternative Hypothesis: mean household income of mall shoppers is greater than $42,500
e) The diameter of a spindle in a small motor is supposed to be 5 mm. If the spindle is either too small or too
large, the motor will not work properly. The manufacturer measures the diameter in a sample of the motors to
determine whether the mean diameter has moved away from the target.
H0:   5 Null Hypothesis: mean diameter of spindle is 5 mm
Ha :
 5
Alternative Hypothesis: mean diameter of spindle is not 5 mm
3) Is the Normality condition safely assumed to be met? Justify.
a) A pharmaceutical manufacturer forms tablets by compressing a granular material that contains the active
ingredient and various fillers. The hardness of a sample from each lot of tablets produced is measured in order
to control the compression process. The hardness data for a sample of 20 tablets are:
11.627
11.613
11.493
11.602
11.360
11.374
11.592
11.458
11.552
11.463
11.383
11.715
11.485
11.509
11.429
11.477
11.570
11.623
11.472
11.531
Since n is small (n=20), I will look at graphs to check for normality.
The histogram and boxplot look slightly skewed to the right, but
there is nothing to suggest that the data is not normally
distributed. The normal probability plot is relatively linear. I
would conclude that the normality condition is met. We would have
to assume that this was a simple random sample, and that the
results were independent of each other (20<10% of total number
of tablets produced) in order to proceed.
b) Bottles of a popular cola are supposed to contain 300 milliliters of cola. There is some variation from bottle
to bottle because the filling machinery is not perfectly precise. In a random sample of 50 bottles, the mean
amount is 299.2 milliliters with standard deviation 4.6 milliliters.
Since n = 50, the Central Limit Theorem says that the distribution of means will be approximately normal. We
will also assume that the sample is SRS and that the fullness of each bottle is independent of any others.
Name: _______________________________________
Hypothesis Worksheet #2
AP Statistics
For each of the following p-values, state whether you would “reject” or “fail to reject” H0 for the given  level.
1) P-value = 0.234 when  = 0.05
Fail Reject H0. Probability of event happening if H0 is
true is greater than 5%.
2) P-value = 0.024 when  = 0.05
Reject H0. Probability of event happening if H0 is true
is less than 5%.
3) P-value = 0.024 when  = 0.01
Fail Reject H0. Probability of event happening if H0 is
true is greater than 1%.
4) P-value = 0.024 when  = 0.10
Reject H0. Probability of event happening if H0 is true
is less than 10%.
For each of the following,
a) draw & shade the curve for Ha
b) calculate the p-value of the given test statistic
5) right-tail test
t = 2.05; n = 20
P(t > 2.05) = 0.027, p-value 0.027
6) left-tail test
z = -1.95; n = 15
P(z <-1.95) = 0.0256, p-value 0.0256
7) two-tail test
t = 1.75; n = 25
P(t< -1.75) or P(t< 1.75) = 2 P(t< -1.75) = 2(.0464) = 0.0929, p = 0.0929
8) two-tail test
t = -2.05; n = 16
P(t< -2.05) or P(t< 2.05) = 2 P(t< -2.05) = 2(.0291) = 0.0583, p = 0.0583
9) During an angiogram, heart problems can be examined via a small tube (a catheter) threaded into the heart
from a vein in the patient’s leg. It’s important that the company who manufacturers the catheter maintain a
diameter of 2.00 mm. Each day, quality control personnel make several measurements to perform a two-tail test
at  = 0.05. For a random sample of 15 measurements, t = 2.056. Calculate the p-value and write the correct
conclusion in context.
H 0:
Ha :
  2.0
  2.0
Null Hypothesis: the mean catheter diameter is 2.00 m
Alternative Hypothesis: the mean catheter diameter is not 2.00 m
P(t< -2.056) or P(t< 2.056) = 2 P(t< -2.056) = 2(.02946) = 0.0589, p = 0.0589
Since the probability of obtaining a t-value of 2.056 is 5.89%, there is not sufficient evidence at the  = 0.05
level to conclude that the mean diameter of the catheters is not 2.00 mm. We do not reject the null
hypothesis.