Question

11 . Choosing the appropriate test statistic You are interested in the difference between two population...

11 . Choosing the appropriate test statistic
You are interested in the difference between two population means. Both populations are normally distributed, and the population variances σ212 and σ222 are known. You use an independent samples experiment to provide the data for your study. What is the appropriate test statistic?
F = √[2/n1 + 2/n2]
F = s1/s2
z = (x̄1 – x̄2) / √[σ2/n1 + σ2/n2]
z = (p̂1 – p̂2) / √[p̂(1 – p̂)(1/n1 + 1/n2)]
Suppose instead that the populations are not normally distributed. The test statistic given is still appropriate provided that    .
You are interested in the difference between two population means. The population variances σ212 and σ222 are unknown and equal. You use an independent samples experiment to generate the data for your study, and each of your samples meet the large sample requirement. What is the appropriate test statistic?
F =√[s21/n1 + s22/n2]
z = (p̂1 – p̂2) / √[p̂(1 – p̂)(1/n1 + 1/n2)]
t = (x̄1 – x̄2) / √[2(1/n1 + 1/n2)]
F = s1/s2
Suppose instead that one (or both) of your samples does not satisfy the large sample requirement. The test statistic given is still appropriate provided that    .
You are interested in the difference between two population means. When is it appropriate to conduct a hypothesis test using the test statistic t = (x̄1x̄1 – x̄2x̄2) / √[2s12/n1n1 + 2s22/n2n2]? Check all that apply.
The population variances σ2 and σ2 are unknown, the data are generated from a matched pairs experiment, and the population of differences are normally distributed.
The populations are both normally distributed, the population variances σ2 and σ2 are unknown and unequal, and the data are generated from an independent samples experiment.
The population variances σ2 and σ2 are known, the data are generated from an independent samples experiment, and both populations are normally distributed.
The population variances σ2 and σ2 are unknown and equal, the data are generated from an independent samples experiment, and both populations are normally distributed.
You want to compar

Homework Answers

Answer #1

A11.

1. c. z = (x̄1 – x̄2) / √[σ2/n1 + σ2/n2]

2. c. t = (x̄1 – x̄2) / √[2(1/n1 + 1/n2)]

3. a. The population variances σ2 and σ2 are unknown, the data are generated from a matched pairs experiment, and the population of differences are normally distributed.

b. The populations are both normally distributed, the population variances σ2 and σ2 are unknown and unequal, and the data are generated from an independent samples experiment.

d. The population variances σ2 and σ2 are unknown and equal, the data are generated from an independent samples experiment, and both populations are normally distributed.

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
In a test of two population means - μ1μ1 versus μ2μ2 - with unknown variances σ21σ12...
In a test of two population means - μ1μ1 versus μ2μ2 - with unknown variances σ21σ12 and σ22σ22, two independent samples of n1=8n1=8 and n2=10n2=10 were taken. The data is given below. Both populations are normally distributed. Sample From Population 1: 11, 7, 14, 14, 19, 16, 16, 16 ; Sample From Population 2: 16, 15, 19, 16, 16, 14, 19, 20, 20, 18 You wish to test the hypothesis that both populations have the same variance. Choose the correct...
Consider the following data from two independent samples with equal population variances. Construct a 90% confidence...
Consider the following data from two independent samples with equal population variances. Construct a 90% confidence interval to estimate the difference in population means. Assume the population variances are equal and that the populations are normally distributed. x1 = 37.1 x2 = 32.2 s1 = 8.9 s2 = 9.1 n1 = 15 n2 = 16
Consider the following hypothesis statement using alphaαequals=0.10 and data from two independent samples. Assume the population...
Consider the following hypothesis statement using alphaαequals=0.10 and data from two independent samples. Assume the population variances are equal and the populations are normally distributed. Complete parts below. H0: μ1−μ2 = 0 x overbar 1 = 14.8 x overbar 2 = 13.0 H1: μ1−μ2 ≠ 0 s1= 2.8 s2 = 3.2 n1 = 21 n2 = 15 a.) what is the test statistic? b.) the critical values are c.) what is the p value?
Consider the test of the claims that the two samples described below come from two populations...
Consider the test of the claims that the two samples described below come from two populations whose means are equal vs. the alternative that the population means are different. Assume that the samples are independent simple random samples and that both populations are approximately normal with equal variances. Use a significance level of α=0.05 Sample 1: n1=18, x⎯⎯1=28, s1=7 Sample 2: n2=4, x⎯⎯2=30, s2=10 (a) Degrees of freedom = (b) The test statistic is t =
Consider the following data from two independent samples with equal population variances. Construct a 98​% confidence...
Consider the following data from two independent samples with equal population variances. Construct a 98​% confidence interval to estimate the difference in population means. Assume the population variances are equal and that the populations are normally distributed. x1=37.9 x2=32.9 s1=8.7 s2=9.2 n1=15 n2=16 Click here to see the t-distribution table page 1, Click here to see the t-distribution table, page 2 The 98​% confidence interval is ​what two numbers. ​(Round to two decimal places as​ needed.)
Given two independent random samples with the following results: n1=13x‾1=72s1=16n1=13x‾1=72s1=16   n2=9x‾2=110s2=31n2=9x‾2=110s2=31 Use this data to find...
Given two independent random samples with the following results: n1=13x‾1=72s1=16n1=13x‾1=72s1=16   n2=9x‾2=110s2=31n2=9x‾2=110s2=31 Use this data to find the 99%99% confidence interval for the true difference between the population means. Assume that the population variances are equal and that the two populations are normally distributed.
You may need to use the appropriate appendix table or technology to answer this question. Consider...
You may need to use the appropriate appendix table or technology to answer this question. Consider the following hypothesis test. H0: μ1 − μ2 = 0 Ha: μ1 − μ2 ≠ 0 The following results are for two independent samples taken from the two populations. Sample 1 Sample 2 n1 = 70 n2 = 60 x1 = 102 x2 = 104 σ1 = 8.6 σ2 = 7.9 (a) What is the value of the test statistic? (b) What is the...
Given two independent random samples with the following results: n1=11x‾1=80s1=28   n2=9x‾2=99s2=18 Use this data to find...
Given two independent random samples with the following results: n1=11x‾1=80s1=28   n2=9x‾2=99s2=18 Use this data to find the 90% confidence interval for the true difference between the population means. Assume that the population variances are equal and that the two populations are normally distributed. Step 1 of 3 : Find the critical value that should be used in constructing the confidence interval. Round your answer to three decimal places
Given two independent random samples with the following results: n1=15 x‾1=109 s1=11 n2=10 x‾2=74 s2=30 Use...
Given two independent random samples with the following results: n1=15 x‾1=109 s1=11 n2=10 x‾2=74 s2=30 Use this data to find the 99% confidence interval for the true difference between the population means. Assume that the population variances are not equal and that the two populations are normally distributed. Step 1 of 3 : Find the critical value that should be used in constructing the confidence interval. Round your answer to three decimal places. If possible, please show work or show...
Given two independent random samples with the following results: n1=11 x‾1=133 s1=20     n2=12 x‾2=151 s2=22 Use...
Given two independent random samples with the following results: n1=11 x‾1=133 s1=20     n2=12 x‾2=151 s2=22 Use this data to find the 90% confidence interval for the true difference between the population means. Assume that the population variances are not equal and that the two populations are normally distributed. Step 1 of 3 : Find the critical value that should be used in constructing the confidence interval. Round your answer to three decimal places. Please show work or show TI 83...
ADVERTISEMENT
Need Online Homework Help?

Get Answers For Free
Most questions answered within 1 hours.

Ask a Question
ADVERTISEMENT