Question

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 112. The plot of the data showed no outliers or cause for concern. Is there sufficient evidence to conclude that the mean quantitative NAAL score for all young adults is less than 290? Use α .05. 27.PLAN: (7 points) Write down the name of the correct procedure to use (2 points), the parameter of interest in the context of the problem (2 points), the null and alternative hypotheses (2 points), and the level of significance you will use (1 point). 字体

Answer 1

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(i) Correct procedure to use: 1 Sample t test

(ii) Parameter of interest: Quantitative NAAL score for young adults

(iii) H0: Null Hypothesis: 290

HA: Alternative Hypothesis: 290

(iv) Level of significance = = 0.05

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(a)

Conditions for the test:

(i) The dependent variable is continuous

(ii) The observations are independent of each other

(iii) The dependent variable is approximately normally distributed

(iv) The dependent variable does not contain any outliers

(b)

How these conditions are met: Explained in the description of the problem.

(c)
SE = s/

= 112/ = 6.2222

Test statistic is:

t = (276 - 290)/6.2222 = - 2.25

(d)

t score = - 2.25

ndf = 324 - 1 = 323

One Tail - Left Side Test

By Technology, P - Value = 0.0126

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Since P - Value is less than , the difference is significant. Reject null hypothesis.

Conclusion:
The data support the claim that mean quantitative NAAL score for all young adults is less than 290.

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95% Confidence Interval: (263.98, 288.02) defines a range of values that we can be 95% certain contains the population mean.