Question

A mixture of pulverized fuel ash and Portland cement to be used for grouting should have...

A mixture of pulverized fuel ash and Portland cement to be used for grouting should have a compressive strength of more than 1300 KN/m2. The mixture will not be used unless experimental evidence indicates conclusively that the strength specification has been met. Suppose compressive strength for specimens of this mixture is normally distributed with σ = 67. Let μ denote the true average compressive strength.

(a) What are the appropriate null and alternative hypotheses?

H0: μ > 1300
Ha: μ = 1300 H0: μ < 1300
Ha: μ = 1300     H0: μ = 1300
Ha: μ ≠ 1300 H0: μ = 1300
Ha: μ > 1300 H0: μ = 1300
Ha: μ < 1300


(b) Let

X

denote the sample average compressive strength for n = 15 randomly selected specimens. Consider the test procedure with test statistic

X

itself (not standardized). What is the probability distribution of the test statistic when H0 is true?

The test statistic has a binomial distribution. The test statistic has a gamma distribution.     The test statistic has an exponential distribution. The test statistic has a normal distribution.


If

X = 1340,

find the P-value. (Round your answer to four decimal places.)
P-value =

Should H0 be rejected using a significance level of 0.01?

reject H0 do not reject H0    


(c) What is the probability distribution of the test statistic when μ = 1350?

The test statistic has a binomial distribution. The test statistic has a normal distribution.     The test statistic has a gamma distribution. The test statistic has an exponential distribution.

State the mean and standard deviation of the test statistic. (Round your standard deviation to three decimal places.)

mean      KN/m2
standard deviation      KN/m2


For a test with α = 0.01, what is the probability that the mixture will be judged unsatisfactory when in fact μ = 1350 (a type II error)? (Round your answer to four decimal places.)

Math   Statistics-And-Probability   
0 0
Add a commentTranscribed image text
Next >

Homework Answers

Answer #1

a)

Ho: μ = 1300
Ha: μ > 1300

b)

test statistic =(x̅-μ)*√n/σ = 2.31
p value = 0.0104

he test statistic has a normal distribution.

do not reject H0    

c(

The test statistic has a normal distribution.

mean= 1350
standard deviation=σ/√n= 17.299
rejection region : x̅ >=μ+z*σ/√n = 1340.307
P(type II error)=P(x̅ <1340.3074)=P(Z<(1340.3074-1350)√15/67)=P(Z<-0.56)= 0.2877
0 0
Know the answer?
Your Answer:

Post as a guest

Your Name:

What's your source?

Earn Coins

Coins can be redeemed for fabulous gifts.

Log In

Sign Up

Not the answer you're looking for?
Ask your own homework help question
Similar Questions
A mixture of pulverized fuel ash and Portland cement to be used for grouting should have...
A mixture of pulverized fuel ash and Portland cement to be used for grouting should have a compressive strength of more than 1300 KN/m2. The mixture will not be used unless experimental evidence indicates conclusively that the strength specification has been met. Suppose compressive strength for specimens of this mixture is normally distributed with σ = 60. Let μ denote the true average compressive strength. (a) What are the appropriate null and alternative hypotheses? (Choose of the following) 1. H0:...
A mixture of pulverized fuel ash and Portland cement to be used for grouting should have...
A mixture of pulverized fuel ash and Portland cement to be used for grouting should have a compressive strength of more than 1300 KN/m2. The mixture will not be used unless experimental evidence indicates conclusively that the strength specification has been met. Suppose compressive strength for specimens of this mixture is normally distributed with σ = 65. Let μ denote the true average compressive strength. (a) What are the appropriate null and alternative hypotheses? H0: μ = 1300 Ha: μ...
A mixture of pulverized fuel ash and Portland cement to be used for grouting should have...
A mixture of pulverized fuel ash and Portland cement to be used for grouting should have a compressive strength of more than 1300 KN/m2. The mixture will not be used unless experimental evidence indicates conclusively that the strength specification has been met. Suppose compressive strength for specimens of this mixture is normally distributed with σ = 59.Let μ denote the true average compressive strength. (a) What are the appropriate null and alternative hypotheses? (b) Let X denote the sample average...
The accompanying data is on cube compressive strength (MPa) of concrete specimens. 112.5      97.0     ...
The accompanying data is on cube compressive strength (MPa) of concrete specimens. 112.5      97.0      92.6      86.0      102.0 99.1      95.8      103.5      89.0      86.6 (a) Is it plausible that the compressive strength for this type of concrete is normally distributed? The normal probability plot is not acceptably linear, suggesting that a normal population distribution is plausible. The normal probability plot is acceptably linear, suggesting that a normal population distribution is plausible.     The normal probability...
Polymer composite materials have gained popularity because they have high strength to weight ratios and are...
Polymer composite materials have gained popularity because they have high strength to weight ratios and are relatively easy and inexpensive to manufacture. However, their nondegradable nature has prompted development of environmentally friendly composites using natural materials. An article reported that for a sample of 10 specimens with 2% fiber content, the sample mean tensile strength (MPa) was 51.5 and the sample standard deviation was 1.3. Suppose the true average strength for 0% fibers (pure cellulose) is known to be 48...
Polymer composite materials have gained popularity because they have high strength to weight ratios and are...
Polymer composite materials have gained popularity because they have high strength to weight ratios and are relatively easy and inexpensive to manufacture. However, their nondegradable nature has prompted development of environmentally friendly composites using natural materials. An article reported that for a sample of 10 specimens with 2% fiber content, the sample mean tensile strength (MPa) was 51.9 and the sample standard deviation was 1.2. Suppose the true average strength for 0% fibers (pure cellulose) is known to be 48...
Polymer composite materials have gained popularity because they have high strength to weight ratios and are...
Polymer composite materials have gained popularity because they have high strength to weight ratios and are relatively easy and inexpensive to manufacture. However, their nondegradable nature has prompted development of environmentally friendly composites using natural materials. An article reported that for a sample of 10 specimens with 2% fiber content, the sample mean tensile strength (MPa) was 51.7 and the sample standard deviation was 1.4. Suppose the true average strength for 0% fibers (pure cellulose) is known to be 48...
The paint used to make lines on roads must reflect enough light to be clearly visible...
The paint used to make lines on roads must reflect enough light to be clearly visible at night. Let μ denote the true average reflectometer reading for a new type of paint under consideration. A test of H0: μ = 20 versus Ha: μ > 20 will be based on a random sample of size n from a normal population distribution. What conclusion is appropriate in each of the following situations? (Round your P-values to three decimal places.) (a)    n =...
Athletes performing in bright sunlight often smear black eye grease under their eyes to reduce glare....
Athletes performing in bright sunlight often smear black eye grease under their eyes to reduce glare. Does eye grease work? In one study, 16 student subjects took a test of sensitivity to contrast after three hours facing into bright sun, both with and without eye grease. This is a matched pairs design. Here are the differences in sensitivity, with eye grease minus without eye grease. 0.06 0.64 −0.12 −0.06 −0.18 0.15 −0.17 0.03 0.04 0.03 0.42 0.25 −0.11 0.28 0.05...
Tree-ring dating from archaeological excavation sites is used in conjunction with other chronologic evidence to estimate...
Tree-ring dating from archaeological excavation sites is used in conjunction with other chronologic evidence to estimate occupation dates of prehistoric Indian ruins in the southwestern United States. Suppose it is thought that a certain pueblo was occupied around 1292 A.D. (based on evidence from potsherds and stone tools). The following data give tree-ring dates (A.D.) from adjacent archaeological sites: 1189 1267 1268 1275 1275 1271 1272 1316 1317 1230 (i) Use a calculator with sample mean and standard deviation keys...
ADVERTISEMENT
Need Online Homework Help?

Get Answers For Free
Most questions answered within 1 hours.

Ask a Question
ADVERTISEMENT