The following information is obtained from two independent samples selected from two populations. n1=270 x¯1=5.98 σ1=1.11 n2=210 x¯2=5.40 σ2=2.47 Test at the 2% significance level if μ1 is greater than μ2 (one-tailed test). μ1 is Choose the answer from the menu in accordance to the question statement μ2 .
To test against
The test statistic can be written as
which under H0 follows a standard normal distribution.
We reject H0 at 2% significance level if P-value < 0.02
Now,
The value of the test statistic =
P-value =
Since P-value < 0.02, so we reject H0 at 2% significance level and we can conclude that μ1 is significantly greater than μ2
The following information is obtained from two independent samples selected from two populations. n1=270 x¯1=5.98 σ1=1.11...
Random samples of sizes n1 = 32 and n2 = 40 are to be drawn from two independent populations. μ1 = 12.3 μ2 = 9.8 σ1 = 2.9 σ2 = 2.4 P(Xbar1 - Xbar 2 < 2) P(S12/ S22 > 2)
The following information was obtained from two indepen- dent samples selected from two normally distributed populations with unknown but equal standard deviations. n1 =21 x ̄=13.97 s1 =3.78 n2 =20 y ̄=15.55 s2 =3.26 Construct a 95% confidence interval for μ1 − μ2.
Two random samples are selected from two independent populations. A summary of the samples sizes, sample means, and sample standard deviations is given below: n1= 37 n2=44 x-bar1= 58.6 x-bar2= 73.8 s1=5.4 s2=10.6 Find a 97% confidence interval for the difference μ1−μ2μ1−μ2 of the means, assuming equal population variances.
Two random samples are selected from two independent populations. A summary of the samples sizes, sample means, and sample standard deviations is given below: n1=51, n2=46, x¯1=57.8, x¯2=75.3, s1=5.2 s2=11 Find a 94.5% confidence interval for the difference μ1−μ2μ1−μ2 of the means, assuming equal population variances. Confidence Interval =
Independent random samples selected from two normal populations produced the sample means and standard deviations shown below: Sample 1 Sample 2 x̅1 = 5.4 x̅2 = 8.2 s1 = 5.6 s2 = 8.2 n1 = 20 n2 = 18 Conduct the test H0 : μ1 - μ2 = 0 against H1 : μ1 - μ2 ≠ 0 ,then the test statistic is __________.
Independent random samples were selected from two normally distributed populations. Given n1 =7 from population 1 and n2=9 from population 2. Population 1: 2.5, 3.1, 2.3, 1.8, 4.2, 3.5, 3.9 Population 2: 2.9, 1.7, 4.6, 3.5, 3.7, 2.8, 4.6, 3.4, 1.9 Find the test statistic for H0 = σ2 = σ2 against HA = σ2 ≠σ2
Suppose we have taken independent, random samples of sizes n1 = 7 and n2 = 7 from two normally distributed populations having means μ1 and μ2, and suppose we obtain x1=240, x2=210, s1=5, and s2 = 6 Use critical values and p-values to test the null hypothesis H0: μ1 − μ2 ≤ 20 versus the alternative hypothesis Ha: μ1 − μ2 > 20 by setting α equal to .10. How much evidence is there that the difference between μ1 and...
Consider the following results for two independent random samples taken from two populations. Sample 1 Sample 2 n1 = 40 n2 = 30 x1 = 13.3 x2 = 11.4 σ1 = 2.2 σ2 = 3.5 a. state the null and alternative hypothesis b. which test should we use for this problem c. what is the test statistic d. what is the critical value e. what is the p-value
Independent random samples of n = 100 observations each are drawn from normal populations. The parameters of these populations are: • Population 1: μ1 = 300 and σ1 = 60; • Population 2: μ2 = 290 and σ2 = 80. (1) What is the probability that the mean of Population 1 is between 294 and 306? (2) How many samples should be included if we want the probability in Part (1) to be at least 95%? (3) What is the...
Independent random samples were selected from two quantitative populations, with sample sizes, means, and standard deviations given below. n1 = n2 = 60 x1 = 125.3 x2 = 123.4 s1 = 5.7 s2 = 6.1 a) Construct a 95% confidence interval for the difference in the population means (μ1 − μ2). (Round your answers to two decimal places.) to b) Find a point estimate for the difference in the population means. c) Calculate the margin of error. (Round your answer...