Question
Asked Oct 14, 2019
376 views

A test is made of H0: u= 50 versus H1: u is greater than 50. A sample of size n=75 is drawn, and mean = 56. The population deviation is"q"=20.

a. Compute the value of the test statistic z.

b. Is H0 rejected at the a=0.05 level?

c. Is H0 rejected at the  a=0.01 level?

check_circle

Expert Answer

Step 1

a)

 

The value of the test statistic is 2.598 and it is obtained below:

 

From the given information, the sample size is 75, mean is 56 and the population standard deviation is 20.

 

Null Hypothesis: H0: µ=50.

Alternative Hypothesis: H1: µ>50.

help_outline

Image Transcriptionclose

х — и Z 56 50 20 75 = 2.598

fullscreen
Step 2

b)

 

Decision Rule:

 

If p-value ≤ α, then reject the null hypothesis.

If p-value > α, then do not reject the null hypothesis.

 

The p-value for the hypothesis testing is 0.0047 and it is obtained below:

help_outline

Image Transcriptionclose

[Since, alternative hypothesis is right tailed] p-value P(z > est) -P(z> 2.60) 1-P(z2.60) 2.60) = 0.995 3] From standard normal table, P(z =1-0.9953 =0.0047

fullscreen
Step 3

Conclusion:

 

From the given information, the level of significance is α=0.05

The p-value is 0.0047.

Here, the p-value is less than the level of significance.

That is, p(=0.0047) < α=0.05.

From the rejecti...

Want to see the full answer?

See Solution

Check out a sample Q&A here.

Want to see this answer and more?

Solutions are written by subject experts who are available 24/7. Questions are typically answered within 1 hour.*

See Solution
*Response times may vary by subject and question.
Tagged in
MathStatistics

Hypothesis Testing

Related Statistics Q&A

Find answers to questions asked by student like you
Show more Q&A
add
question_answer

Q: question 9 c

A: 9(c) The formula to calculate probability is,

question_answer

Q: In a certain shipment of 19 computers, 11 are defective. 7 of the computers are selected at random w...

A: Given dataTotal computers = 19No of defectives = 11

question_answer

Q: A study is run to estimate the mean total cholesterol level in children 9-11 years of age. A sample ...

A: It is given that the average cholesterol level is 160.5 and population standard deviation is 18.

question_answer

Q: The question again: A two-factor ANOVA produces an F-ratio for A with df = 1, 36 and an F - ratio fo...

A: Hello There ! there are more than one question. According to our policies we cannot answer more than...

question_answer

Q: assume that a procedure yields a binomial distrobution with a trial repeated n times. Use the binomi...

A: Consider,Let x be a random variable that follows the binomial distribution.

question_answer

Q: Do larger states have a higher graduation rate? If not explain why

A: The Five-Number Summary:Minimum:The minimum observation in a data set is the observation with the sm...

question_answer

Q: 74% of all students at a college still need to take another math class. If 37 students are randomly ...

A: (a) The probability that at exactly 25 students need to take another math class is 0.0951 and it is ...

question_answer

Q: On a particular night, a baseball stadium sells 60% of its seats, and of those, 15% do not end up sh...

A: According to the provided data, 60% of the seats are booked and 15% of these do not end up showing, ...

question_answer

Q: A study is run to estimate the mean total cholesterol level in children 9-11 years of age. A sample ...

A: According to provided data, the sample mean is 160.3, the population standard deviation is 18.2 and ...