Question

A group of third grade students is taught using a new curriculum. A control group of third grade Old Curriculum New Curriculum 6 3 72 4 8 students is taught using the old curriculum. The reading test scores for the two groups are shown in 88554310 5 68 the back-to-back stem-and-leaf plot. At a 0.10, is 987544106 00 1255688899 there enough evidence to support the claim that the new method of teaching reading produces higher reading test scores than the old method does? Assume the population variances are equal Complete parts (a) through (e) below. Assume the samples are random and independent, and the populations are normally distributed. 7 11224678 8 49 74 Old and 70 New Key: 41710 (a) Identify the claim and state Ho and H, Which is the correct claim below? 0 A, O B. "The new method of teaching reading produces equal reading test scores as the old method "The new method of teaching reading produces lower reading test scores than the old method." O C. "The new method of teaching reading produces different reading test scores than the old method." O D. The new method of teaching reading produces higher reading test scores than the old method. Click to select your answer(s) 8 49 Key: 4170-74 Old and 70 New reading test scores than the old method does? Assume the population variances are equal Complete parts (a) through (e) below. Assume the samples are random and independent, and the populations are normally distributed. What are Ho and Ha? Assume that μι represents the mean of the test scores of those taught with the old curriculum and μ2 represents the mean rom the new curm The null hypothesis, Ho, is Which hypothesis is the claim? O The null hypothesis, Ho Click to select your answer(s) lent the arm V The alternative hypothesis, Ha, is populations are normally distributed. Enter the critical value(s) below. (Type an integer or decimal rounded to three decimal places as needed. Use a comma to separate answers as needed.) Select the correct rejection region(s) below Click to select your answer(s). (c) Find the standardized test statistic. (Type an integer or decimal rounded to three decimal places as needed.) (d) Decide whether to reject or fail to reject the null hypothesis. the null hypothesis Click to select your answer(s).

Answer 1

Solution:-

New Old Mean Standard Error Median Mode Standard Deviation 8.932168 Standard Deviation Sample Variance79.78363 Sample Variance Kurtosis Skewness Range Minimum Maximum Sum Count 56.68421 Mean 68.28 1.782807 68 68 8.914034 79.46 0.673439 0.129323 41 48 89 1707 25 2.04918 Standard Error 58 Median 55 Mode 0.125106 Kurtosis 0.66138 Skewness 33 Range 36 Minimum 69 Maximum 1077 Sum 19 Count

a) (D) The new method of teaching produces higher reading test scores than the old method.

State the hypotheses. The first step is to state the null hypothesis and an alternative hypothesis.

Null hypothesis: u₁> u₂
Alternative hypothesis: u₁ < u₂

Note that these hypotheses constitute a one-tailed test.

Formulate an analysis plan. For this analysis, the significance level is 0.10. Using sample data, we will conduct a two-sample t-test of the null hypothesis.

Analyze sample data. Using sample data, we compute the standard error (SE), degrees of freedom (DF), and the t statistic test statistic (t).

SE = sqrt[(s₁²/n₁) + (s₂²/n₂)]
SE = 2.71616
DF = 42
t_critical = - 1.302

Rejection region is t < - 1.302

p = 0.1 -4 -3 -2 -1 4 t--1.302

c)

t = [ (x₁ - x₂) - d ] / SE

t = - 4.269

where s₁ is the standard deviation of sample 1, s₂ is the standard deviation of sample 2, n₁ is the size of sample 1, n₂ is the size of sample 2, x₁ is the mean of sample 1, x₂ is the mean of sample 2, d is the hypothesized difference between population means, and SE is the standard error.

Interpret results. Since the t-value(-4.269) lies in the rejection region, hence we have to reject the null hypothesis.

d) Reject the null hypothesis.