A random sample of 86 eighth grade students scores on a national mathematics ass
ID: 3234374 • Letter: A
Question
A random sample of 86 eighth grade students scores on a national mathematics assess test has a mean score of 287. This test result prompts a state school administrator to declare that the mean score for the state's eighth graders on this exam is more than 285. Assume that the population standard deviation is At alpha = 0.14, is there enough evidence to support the administrator's claim? Complete parts (a) through (a). (a) Write the claim mathematically and identity H_0 and H_a. choose the correct answer below. A. H_0: mu = 285 H_a: mu > 285(claim) B. H_0: mu greaterthanorequalto 285(claim) H_a: = mu 285(claim) F. H_0: mu 285 (b) Find the standardized test statistic z, and its corresponding area z = (Round to two decimal places as needed)Explanation / Answer
Solution:-
State the hypotheses. The first step is to state the null hypothesis and an alternative hypothesis.
Null hypothesis: < 285
Alternative hypothesis: > 285
Note that these hypotheses constitute a one-tailed test. The null hypothesis will be rejected if the sample mean is too small.
Formulate an analysis plan. For this analysis, the significance level is 0.14. The test method is a one-sample z-test.
Analyze sample data. Using sample data, we compute the standard error (SE) and the z statistic test statistic (z).
SE = s / sqrt(n)
S.E = 3.67
z = (x - ) / SE
z = 0.55
where s is the standard deviation of the sample, x is the sample mean, is the hypothesized population mean, and n is the sample size.
The observed sample mean produced a z statistic test statistic of 0.545. We use the normal Distribution Calculator to find P(z > 0.545) = 0.2912
Interpret results. Since the P-value (0.2912) is greater than the significance level (0.14), we cannot reject the null hypothesis.
From the above test we do not have sufficient evidence in the favor of the administrator's claim.
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