Question

Suppose that someone claims that the mean income of two group of individuals is equal. In...

Suppose that someone claims that the mean income of two group of individuals is equal. In order to test that claim, a researcher collects two samples and finds that the one group earns $1,448 more on average than the other group. Is that sufficient evidence to reject the claim that the mean income in the two populations is equal?

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

Homework Answers

Answer #1

NO, that is not sufficient evidence to reject the claim that the mean income of the two populations is equal. Just comparing means and seeing that the mean of one group is greater than the other is not enough to determine whether the population mean income for the two groups is different or the same.

To understand this, lets look at the test statistics, which would be :-

Looking at the denominator, this test statistic is highly dependent upon the sample standard deviations for the two groups. So even if the mean difference seems high, if the standard deviations are high enough then the value of the above statistic would be reduced and on further testing, there is a chance that we conclude that the mean income of the populations are the same.

Let me know in comments if anything is not clear. Will reply ASAP. Please do upvote if satisfied.

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
Suppose that someone claims that the mean income of two group of individuals is equal. In...
Suppose that someone claims that the mean income of two group of individuals is equal. In order to test that claim, a researcher collects two samples and finds that the one group earns $1,448 more on average than the other group. Is that sufficient evidence to reject the claim that the mean income in the two populations is equal? why?
A study was done using a treatment group and a placebo group. The results are shown...
A study was done using a treatment group and a placebo group. The results are shown in the table. Assume that the two samples are independent simple random samples selected from normally distributed​ populations, and do not assume that the population standard deviations are equal. Complete parts​ (a) and​ (b) below. Use a 0.05 significance level for both parts. Treatment Placebo u u1 u2 n 34 30 x 2.34 2.62 s 0.58 0.95 1. The test statistic is _____ (round...
A study was done using a treatment group and a placebo group. The results are shown...
A study was done using a treatment group and a placebo group. The results are shown in the table. Assume that the two samples are independent simple random samples selected from normally distributed​ populations, and do not assume that the population standard deviations are equal. Complete parts​ (a) and​ (b) below. Use a 0.10 significance level for both parts. Treatment Placebo mu mu 1 mu 2 n 29 40 x overbar 2.34 2.69 s 0.82 0.52 a. Test the claim...
An advertising executive claims that there is a difference in the mean household income for credit...
An advertising executive claims that there is a difference in the mean household income for credit cardholders of Visa Gold and of MasterCard Gold. A random survey of 13 Visa Gold cardholders resulted in a mean household income of $68,600 with a standard deviation of $9200. A random survey of 8 MasterCard Gold cardholders resulted in a mean household income of $59,620 with a standard deviation of $10,900. Is there enough evidence to support the executive's claim? Let μ1 be...
A pet association claims that the mean annual cost of food for dogs and cats are...
A pet association claims that the mean annual cost of food for dogs and cats are the same. The results for samples for the two types of pets are shown below. Is there enough evidence at ? = 0.05 to reject the pet association’s claim? Assume the population variances are not equal. Assume the samples are random and independent and the populations are normally distributed. Dogs Cats ?̅̅1̅ = $210    ?̅̅2̅ = $187 ?1 = 35 ?1 = 31 ?1...
An advertising executive claims that there is a difference in the mean household income for credit...
An advertising executive claims that there is a difference in the mean household income for credit cardholders of Visa Gold and of MasterCard Gold. A random survey of 18 Visa Gold cardholders resulted in a mean household income of $84,280 with a standard deviation of $10,400. A random survey of 11 MasterCard Gold cardholders resulted in a mean household income of $79,360 with a standard deviation of $9800. Is there enough evidence to support the executive's claim? Let μ1 be...
A credit card company claims that the mean credit card debt for individuals is greater than...
A credit card company claims that the mean credit card debt for individuals is greater than $5,000. You want to test this claim. You find that a random sample of 33 cardholders has a mean credit card balance of $5,232 and a standard deviation of $675. At alpha α= 0.01​ can you support the​ claim? Complete parts​ (a) through​ (e) below. Assume the population is normally distributed.​ (a) Write the claim mathematically and identify H0 and Ha. Which of the...
Colonial funds claims to have a bond fund which has maintained a mean share price of...
Colonial funds claims to have a bond fund which has maintained a mean share price of $15.00. They claim that the standard deviation of the share price is 0.24. To test this claim, the investor randomly selects 16 days during the last year. He finds an average share price of $14.80 with a standard deviation of 0.171. Can the investor conclude that the share price of the bond fund varies by less than colonial funds claims at a=0.025? Step 1...
An administrator claims that the average test scores between two instructors at a school are different....
An administrator claims that the average test scores between two instructors at a school are different. In a sample of 28 students from the first instructor’s class, the average test score was 32 out of 50 points with a standard deviation of 5 points. In a sample of 33 students from the second instructor’s class, the average was 29 out of 50 with a standard deviation of 6 points. Assuming both populations are normally distributed and the population variances are...
Test the claim that the proportion of children from the low income group that drew the...
Test the claim that the proportion of children from the low income group that drew the nickel too large is greater than the proportion of the high income group that drew the nickel too large. Test at the 0.05 significance level. 18 of 40 children in the low income group drew the nickel too large, and 13 of 35 did in the high income group. a) If we use LL to denote the low income group and HH to denote...
ADVERTISEMENT
Need Online Homework Help?

Get Answers For Free
Most questions answered within 1 hours.

Ask a Question
ADVERTISEMENT