Description
Show your work (if appropriate) for full credits. Submit your answer in pdf format to blackboard.
1. To obtain information on the corrosion-resistance properties of a certain type of steel conduit,
35 specimens are buried in soil for a 2-year period. The penetration (in mils) for each specimen
is then measured, yielding a sample mean penetration of 𝑥̄= 35.7and a sample standard
deviation of s=4.2.
A. Suppose the true population standard deviation is σ=5. Construct a 90% confidence interval
for the true average penetration for this type of steel conduit. Interpret the interval.
B. Now suppose the true standard deviation is unknown. Construct a 90% confidence interval
for the true average penetration for this type pf steel conduit. Interpret the interval.
2. The recommended daily dietary allowance for zinc among males older than age 50 years is 15
mg/day. A study reports the following summary data on intake for a sample of males age 65–74
years: n=20, 𝑥̄= 10.23, and s=5.17. The scientist wants to know if this data indicates that
average daily zinc intake in the population falls below the recommended allowance.
A. The QQ plot is provided on the right and Shapiro-Wilk normality test is provided. Use
this to assess if it is plausible to assume that the daily zinc intake is normally distributed.
Briefly explain your answer.
Shapiro-Wilk normality test
data: x
W = 0.95112, p-value = 0.3844
R commands:
x=c(9.41, 20.06, 8.80, 10.10, 14.38, 10.42, 13.30, 4.04, 3.40, 11.95, 12.77, 6.39, 21.95, 14.82,
12.75, 8.86, 5.56, 6.26, 6.52, 2.81)
qqnorm(x)
shapiro.test(x) # Test of H0: {Data come from a normal distribution.}
B. Carry out the test of H0: μ=15 vs Ha: μ<15 at α=0.05. Make sure you calculate the test
statistic, define the rejection region, and make a decision about the test. You can check
your conclusion with R command: t.test(x,mu=15,alternative=”less”)
3. A pollution-control inspector suspected that a riverside community was releasing semi-treated
sewage into a river and this, as a consequence, was changing the level of dissolved oxygen of
the river. To check this, he drew 45 randomly selected specimens of river water at a location
above the town and another 45 specimens below. The sample information for the measured
oxygen level by groups are given blow.
Sample mean sd n
Above 4.83 0.175 45
Below 4.55 0.234 45
A. Construct a 90% two-sided confidence interval for the difference between the average
dissolved oxygen levels above town and below town. Does the data provide evidence to
indicate a difference in the true average dissolved oxygen between locations above and
below town?
B. The scientist wants to know if the average oxygen level below town is higher than above
town. Run a hypothesis test at significance level α=0.05. Use the 4-step procedure: 1:
State the null and alternative hypotheses. 2:Give the test statistic, 3 find the rejection
region or the p-value, and 4: make a decision.
