Question

Looking at my answers, I was am always off buy about range of .1 to .4...

Looking at my answers, I was am always off buy about range of .1 to .4 from the correct answer that is stated. I am having a really tough time trying to figure out how to get my number to be exactly like what is shown as correct so I need a little help with figuring out what I am doing wrong. Here is an example of a question I just cant seem to figure out. I'll show all my steps and let me know what I am doing wrong please

Construct a  90% confidence interval to estimate the population mean using the data below.
x̅ =50 σ=10 n=20 N=200

The  90% confidence interval for the population mean is (___, ___)
(Round to two decimal places as needed.)

My steps:
UCL = x̅ + (critical z-value)(σ)
LCL = x̅ - (critical z-value)(σ)

So I find σx̅

σ = σ/√n σ = 10/√20 = 2.236

Finding Critical z - value
α = (1 - confidence interval) then divide by 2 (1 - .90)/2 = .05 then using technology I find the z-value of .05 = 1.645

Plug it all in
50 + (1.645)(2.236) = 53.68
50 - (1.645)(2.236) = 46.32

I then have an answer that the 90% confidence interval for the population mean is (46.32, 53.68) which is incorrect. The correct answer shown is (46.50, 53.50) but I am unsure how to get this interval. Could someone work this out and show me the steps on how to get the correct interval please?

Homework Answers

Answer #1

Note: The 90% confidence interval is (46.3217 , 53.6783) . Your answer and all the steps are correct. There may be some error in the given data or the answer.

We need to construct the 90% confidence interval for the population mean μ. The following information is provided:

x̅ =50, σ=10 and   n=20

The critical value for α=0.1 is Zc​=Z1−α/2 ​= 1.645. The corresponding confidence interval is computed as shown below:

  

  

  

Know the answer?
Your Answer:

Post as a guest

Your Name:

What's your source?

Earn Coins

Coins can be redeemed for fabulous gifts.

Not the answer you're looking for?
Ask your own homework help question
Similar Questions
I am doing a stats project and I'm determining confidence levels for my survey. I used...
I am doing a stats project and I'm determining confidence levels for my survey. I used a simple random sample by sending an email out to my population of 306 people and only 25 responded. When determining a confidence interval to a yes or no question, do I use the sample number for my n, which would be 25, or do I use the total population in which I was targeting for my n, which would be 306?
I am having an issue with my Statistics teacher and I am hoping a friend here...
I am having an issue with my Statistics teacher and I am hoping a friend here could clarify. I have enclosed the question I was marked wrong on. Notice the question asks for the LOWER CHI-SQUARE SCORE. Is that appropriate? There is only one CHI-SQUARE SCORE for this problem. But is it appropriate to refer to it as 'lower'? Please review and answer this: The following is a random sample of the volt measurements of a solar panel taken at...
You calculate a one-tailed z-test and find that for your study, z = 1.40, p >...
You calculate a one-tailed z-test and find that for your study, z = 1.40, p > .05. A. What is the proportion of the curve that is in the critical region? B. Is this a Type I or Type II error? C. Do you reject or fail to reject the null hypothesis? D. What is the confidence interval? For a normal distribution with a population mean μ of 80 and a population standard deviation (σ) of 50, find each probability...
Biologists studying the healing of skin wounds measured the rate at which new cells closed a...
Biologists studying the healing of skin wounds measured the rate at which new cells closed a cut made in the skin of an anesthetized newt. Here are data from a random sample of 18 newts, measured in micrometers (millionths of a meter) per hour: 29, 27, 34, 40, 22, 28, 14, 35, 26, 35, 12, 30, 23, 18, 11, 22, 23, 33 (a) Create a QQ plot of the data. Do you think it is reasonable to assume that the...
Is this correct? My claims is that 30% of coffee drinkers consume more than 1 cup...
Is this correct? My claims is that 30% of coffee drinkers consume more than 1 cup of coffee per day. I asked 30 people if they consume more than 1 cup of coffee per day and 14 people stated they consume more than 1 cup of coffee per day. 1. Make a claim. 30% of coffee drinkers drunk more than 1 cup of coffee per day 2. Check the conditions and see if the requirements are met. H0: p =0.30...
Using the table below, would you please check my answers. The answer for the p-value is...
Using the table below, would you please check my answers. The answer for the p-value is supposed to be 0.0000; however, I keep getting 0.9999999977 as the answer. How do you find the correct p-value? Where am I going wrong in my calculation? Regardless of your answer to part (a) using R, run a t-test for the difference between the two treatment means at the α = 5% level of significance. Specifically, we are interested in knowing if there exists...
Think about a population mean that you may be interested in and propose a hypothesis test...
Think about a population mean that you may be interested in and propose a hypothesis test problem for this parameter. Gather appropriate data and post your problem and solution in the discussion topic. For example, you may believe that the population mean number of times that adults go out for dinner each week is less than 1.5. Your data could be that you spoke with 7 people and found that they went out 2, 0, 1, 5, 0, 2, and...
1. I am interested in if there is a pay difference between men and women nurses....
1. I am interested in if there is a pay difference between men and women nurses. Based on a study by ucsf male nurses used to make more.  I randomly sample and collect data. Assume you can pool the variances. What is the p-value based on the following sample... Females Males xbar 44,000 47,000 s 12,000 12,600    n 60 57 What is the p-value? 2. I am interested in if there is a pay difference between men and women nurses....
1.) What is the critical z value of a two sided test for alpha = .01?...
1.) What is the critical z value of a two sided test for alpha = .01? A.) 2.33 B.) 2.57 C.) 0.004 D.) 0.040 2.) Mocha Joe has n = 23, a sample average of 1,000,000, and a sample standard deviation of 350,000. What t-value should Mocha Joe use for a 95% confidence interval? A.) 1.960 B.) 2.064 C.) 2.069 D.) 2.074 3.) What is the center of a confidence interval? A.) µ B.) s C.) x̄ D.) σ 4.)...
TRUE OR FALSE: 1. The sampling distribution of (X-bar) is always a normal distribution according to...
TRUE OR FALSE: 1. The sampling distribution of (X-bar) is always a normal distribution according to the Central limit theorem. 4. If the sampled population is a normal distribution, then the sampling distribution of   (X-bar is normal only for a large enough sample size. 5. If p=.8 and n=50, then we can conclude that the sampling distribution of the proportions is approximately a normal distribution. 8. Assuming the same level of significancea, as the sample size increases, the critical t-value...
ADVERTISEMENT
Need Online Homework Help?

Get Answers For Free
Most questions answered within 1 hours.

Ask a Question
ADVERTISEMENT