14)
a) Two sample t test is used to compare the means assuming equal variance. The test is performed in following steps,
Step i: The Null and Alternative Hypotheses
The significance level is for the test .
Step ii:
The sample follows the normal distribution.
Assumption: the sampling distribution of mean should be approximately normal. And a sample distribution can be approximate to its population if the sample size is sufficiently large such that
Also sampling distribution requires independence of the observations in the sample
test-statistic
The t-statistic is computed as follows:
From the data given,
Age | mean | n | s |
>65 | 15.2 | 32 | 7.2 |
25-34 | 19.7 | 35 | 5.2 |
Step iii: Since, the P-value is obtained from t distribution table for the t-statistic = -2.951 and
degree of freedom, df = n1+n2-2= 32+35-2=65
Step iv: Since the P-value is less than 0.05 at 5% significant level, it can be concluded that the null hypothesis is rejected.
Step v: There is a significantly better educated younger generation.
b)
The confidence interval for the difference in means is obtained as follow,
Where,
The critical value for this left-tailed test is obtained from t critical value table for and degree of freedom, df = n1+n2-2= 32+35-2=65
18)
a) Two sample t test is used to compare the means assuming equal variance. The test is performed in following steps,
Step i: The Null and Alternative Hypotheses
The significance level is for the test .
Step ii:
The sample follows the normal distribution.
Assumption: the sampling distribution of mean should be approximately normal. And a sample distribution can be approximate to its population if the sample size is sufficiently large such that
Also sampling distribution requires independence of the observations in the sample
test-statistic
The t-statistic is computed as follows:
From the data given,
mean | n | s | |
Experimental group | 368.4 | 30 | 39.5 |
Control group | 349.2 | 30 | 56.6 |
Step iii: Since, the P-value is obtained from t distribution table for the t-statistic = 1.524 and
degree of freedom, df = n1+n2-2= 30+30-2=58
Step iv: Since the P-value is greater than 0.01 at 1% significant level, it can be concluded that the null hypothesis is not rejected.
Step v: There is no difference in experimental and control group mean.
b)
The confidence interval for the difference in means is obtained as follow,
Where,
The critical value for this left-tailed test is obtained from t critical value table for and degree of freedom, df = n1+n2-2= 30+30-2=58
both questions plz 14. Generation Gap: Education Education influences attitude and lifestyle. nowDifferences in education are...
Education influences attitude and lifestyle. Differences in education are a big factor in the "generation gap." Is the younger generation really better educated? Large surveys of people age 65 and older were taken in n1 = 30 U.S. cities. The sample mean for these cities showed that x1 = 15.2% of the older adults had attended college. Large surveys of young adults (age 25–34) were taken in n2 = 39 U.S. cities. The sample mean for these cities showed that...
Education influences attitude and lifestyle. Differences in education are a big factor in the generation gap." is the younger generation really better educated? Large surveys of people age 65 and older were taken in n - 34 U.S. cities. The sample mean for these cities showed that #1 - 15.2% of the older adults had attended college. Large surveys of young adults (age 25 34) were taken in ny = 32 U.S. cities. The sample mean for these cities showed...
Education influences attitude and lifestyle. Differences in education are a big factor in the generation gap." Is the younger generation really better educated? Large surveys of people age 65 and older were taken in ny - 39 U.S. cities. The sample mean for these cities showed that X1 - 15.2% of the older adults had attended college. Large surveys of young adults (age 25 - 34) were taken in n2-30 U.S. cities. The sample mean for these cities showed that...
Education influences attitude and lifestyle. Differences in education are a big factor in the "generation gap." Is the younger generation really better educated? Large surveys of people age 65 and older were taken in n - 37 U.S. cities. The sample mean for these cities showed that xı -15.2% of the older adults had attended college. Large surveys of young adults (age 25 - 34) were taken in 12 - 33 U.S. cities. The sample mean for these cities showed...
Two researchers conducted a study in which two groups of students were asked to answer 42 trivia questions from a board game. The students in group 1 were asked to spend 5 minutes thinking about what it would mean to be a professor, while the students in group 2 were asked to think about soccer hooligans. These pretest thoughts are a form of priming. The 200 students in group 1 had a mean score of 26.2 with a standard deviation...
Use this information to answer the next four questions. Some educators claim that the average young person can't even calculate a 15% tip. The National Assessment Adult Literacy (NAAL) survey indicates that a score of 290 or higher on its quantitative test reflect skills that include those needed to calculate a tip. The NAAL administered the test to a random sample of 324 young adults (aged 19 to 24). The survey data yielded a mean of 276 and standard deviation...
plz help with all questions 180-2100 I. Multiple-choice (Circle the letter of your answer): = 100 and (1) For a continuous random variable 1, the population mean and standard deviation are o 20 respectively. the mean jy and the standard deviation og of the sample mean for a random sample of 16 items from this population are ( 5 0.05) (A) Pa = 25, ; 20 (B) P = 100, -20 (C) = 25,0 = 5 (D) Hg = 100,...
1. In an August 2012 Gallup survey of 1,012 randomly selected U.S. adults (age 18 and over), 53% said that they were dissatisfied with the quality of education students receive in kindergarten through grade 12. The bootstrap distribution (based on 5,000 samples) is provided. a). Would it be appropriate to use the normal distribution to construct the confidence interval in this situation? Explain briefly. b). The standard error from the bootstrap distribution is SE = 0.016. Use the normal distribution...
(a) Determine the test statistic (t = ?). Round to two decimal places as needed. (b) Construct a 90% confidence interval for μcommunity college − μno transfer to approximate the mean additional time it takes to complete a bachelor's degree if you begin in community college. The bounds of a (1 − α) • 100% confidence interval about μ1 − μ2 can be found using the following formulas, where tα/2 is the critical value. Round to six decimal places as...
Education officials in a particular state claim that their state is especially effective in preparing students for college. One assessment of preparation for college is the mathematics part of the Scholastic Aptitude Test (SAT-Math). Suppose that one wanted to infer the population mean SAT-Math score for students in this state using the mean of a simple random sample of SAT-Math scores of students from this state, and one knew that the population standard deviation σ = 100‡. sample mean: 525...