Question

ch 21 the 2013 national assessment of educational progress (naep) gave a mathematics test to a random sample of twelfth - graders in michigan. the mean score was 154 out of 300. to give a confidence interval for the mean score of all michigan twelfth - graders, you would use the two - sample t interval. the matched pairs t interval. the one - sample t interval. question 19 1 pts ch 21 we suspect that younger adults use social media more than adults aged 40 or over. to see if this is true, test these hypotheses for the mean social media usage scores of all adults under 40 and all adults 40 and over: ( h_0:mu_{<40}=mu_{geq40} ) versus ( h_a:mu_{<40}
eqmu_{geq40} ) ( h_0:mu_{<40}=mu_{geq40} ) versus ( h_a:mu_{<40}<mu_{geq40} ) ( h_0:mu_{<40}=mu_{geq40} ) versus ( h_a:mu_{<40}>mu_{geq40} )

Explanation:

• For the first question:
• The one - sample \(t\) interval is used when we want to estimate the population mean based on a single sample. Here, we have a single sample of twelfth - graders in Michigan and want to estimate the mean score of all Michigan twelfth - graders.
• The two - sample \(t\) interval is for comparing means of two independent samples. The matched pairs \(t\) interval is for paired data (e.g., before - and - after measurements on the same subjects).
• For the second question:
• The null hypothesis \(H_0:\mu_{<40}=\mu_{\geq40}\) is the statement of no difference.
• The alternative hypothesis \(H_a:\mu_{<40}>\mu_{\geq40}\) is correct because we suspect that younger adults (under 40) use social media more (i.e., have a higher mean social media usage score) than adults 40 or over. If \(H_a:\mu_{<40}

eq\mu_{\geq40}\), it just says there is a difference (could be either way). If \(H_a:\mu_{<40}<\mu_{\geq40}\), it would mean younger adults use social media less, which is contrary to our suspicion.

Answer:

• First question: the one - sample \(t\) interval.
• Second question: \(H_0:\mu_{<40}=\mu_{\geq40}\) versus \(H_a:\mu_{<40}>\mu_{\geq40}\)