Suppose a consumer product researcher wanted to find out whether a highlighter lasted less than the manufacturer's claim that their highlighters could write continuously for 14 hours. The
Researcher tested 40 highlighters and recorded the number of continuous hours each highlighter
Wrote before drying up. Test the hypothesis that the highlighters wrote for less than 14 continuous
Hours. Following are the summary statistics: $$\bar { x } = 13.6 \text { hours, } s = 1.3 \text { hours }$$ Report the test statistic, p-value, your decision regarding the null hypothesis, and your conclusion
About the original claim. Round all values to the nearest thousandth.
A) $\mathrm { z } = 1.946 ; \mathrm { p } = 0.974$; Fail to reject the null hypothesis; there is not strong evidence to suggest that the highlighters last less than 14 hours.
B) $z = 1.946 ; \mathrm { p } = 0.029$; Reject the null hypothesis; there is strong evidence to suggest that the highlighters last less than 14 hours.
C) $t = - 1.946 ; p = 0.029$; Fail to reject the null hypothesis; there is not strong evidence to suggest that the highlighters last less than 14 hours.
D) $t = - 1.946 ; p = 0.029$; Reject the null hypothesis; there is strong evidence to suggest that the highlighters last less than 14 hours.

Question

Suppose a consumer product researcher wanted to find out whether a highlighter lasted less than the manufacturer's claim that their highlighters could write continuously for 14 hours. The
Researcher tested 40 highlighters and recorded the number of continuous hours each highlighter
Wrote before drying up. Test the hypothesis that the highlighters wrote for less than 14 continuous
Hours. Following are the summary statistics: $$\bar { x } = 13.6 \text { hours, } s = 1.3 \text { hours }$$ Report the test statistic, p-value, your decision regarding the null hypothesis, and your conclusion
About the original claim. Round all values to the nearest thousandth. 
A) $\mathrm { z } = 1.946 ; \mathrm { p } = 0.974$; Fail to reject the null hypothesis; there is not strong evidence to suggest that the highlighters last less than 14 hours.
B) $z = 1.946 ; \mathrm { p } = 0.029$; Reject the null hypothesis; there is strong evidence to suggest that the highlighters last less than 14 hours.
C) $t = - 1.946 ; p = 0.029$; Fail to reject the null hypothesis; there is not strong evidence to suggest that the highlighters last less than 14 hours.
D) $t = - 1.946 ; p = 0.029$; Reject the null hypothesis; there is strong evidence to suggest that the highlighters last less than 14 hours.

Quizplus · Accepted Answer

The test statistic is calculated using the t-distribution because the sample size is less than 30. The calculated t-value is -1.946, and the p-value is 0.029. Since the p-value is less than the typical significance level of 0.05, we reject the null hypothesis, indicating strong evidence that the highlighters last less than 14 hours.

Suppose a Consumer Product Researcher Wanted to Find Out Whether xˉ=13.6 hours, s=1.3 hours \bar { x } = 13.6 \text { hours, } s = 1.3 \text { hours }xˉ=13.6 hours, s=1.3 hours

Suppose a Consumer Product Researcher Wanted to Find Out Whether $\bar { x } = 13.6 \text { hours, } s = 1.3 \text { hours }$