Question

a group of third grade students is taught using a new curriculum. a control group of third grade students is taught using the old curriculum. the reading test scores for the two groups are shown in the back - to - back stem - and - leaf plot. at \\(\alpha = 0.10\\), is 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. old curriculum new curriculum 7 3 4 0 4 8 9 9 7 6 6 3 3 0 5 1 2 9 8 6 4 2 1 0 0 6 0 0 1 2 2 3 5 5 8 8 8 9 7 0 0 1 5 6 6 8 9 8 3 8 key: 4|7|0 = 74 old and 70 new (a) identify the claim and state \\(h_0\\) and \\(h_a\\). which is the correct claim below? \\(\bigcirc\\) a. \the new method of teaching reading produces lower reading test scores than the old method.\ \\(\bigcirc\\) b. \the new method of teaching reading produces higher reading test scores than the old method.\ \\(\bigcirc\\) c. \the new method of teaching reading produces different reading test scores than the old method.\ \\(\bigcirc\\) d. \the new method of teaching reading produces equal reading test scores as the old method.\ what are \\(h_0\\) and \\(h_a\\)? assume that \\(\mu_1\\) represents the mean of the test scores of those taught with the old curriculum \\(\mu_2\\) represents the mean from the new curriculum. identify the claim. the null hypothesis, \\(h_0\\), is \\(\boldsymbol{\
abla}\\) the alternative hypothesis, \\(h_a\\), is \\(\boldsymbol{\
abla}\\)

Explanation:

The problem is about testing a claim regarding the mean reading scores of two groups (old vs new curriculum). The claim is that the new method produces higher scores, so we compare the means. The null hypothesis ($H_0$) is the statement of no difference or equality, and the alternative hypothesis ($H_a$) is the claim we are testing. Since the claim is that the new method (μ₂) has higher scores than the old (μ₁), we set $H_0: \mu_1 \geq \mu_2$ (null, assuming no improvement or worse) and $H_a: \mu_1 < \mu_2$ (alternative, the claim that new is higher, so old mean is less than new mean). For the claim identification, option B matches the statement "the new method... produces higher... scores than the old method".

Answer:

The correct claim is B. "The new method of teaching reading produces higher reading test scores than the old method."
$H_0: \mu_1 \geq \mu_2$
$H_a: \mu_1 < \mu_2$ (The claim is represented by $H_a$ as it states the new method (μ₂) has a higher mean than the old (μ₁), so μ₁ < μ₂ is the alternative hypothesis, and the null is the opposite or equality.)