Answer: No , at 0.05 level of significance , we have sufficient evidence to reject the claim that LTCC Intermediate Algebra students get less than seven hours of sleep per night, on average.
Step-by-step explanation:
Let [tex]\mu[/tex] denotes the average hours of sleep per night.
As per given , we have
[tex]H_0:\mu=7\\H_a:\mu<7[/tex]
, since [tex]H_a[/tex] is left-tailed and population standard deviation is unknown, so the test is a left-tailed t -test.
Also , it is given that ,
Sample size : n= 22
Sample mean : [tex]\overline{x}=7.24[/tex]
Sample standard deviation : s= 1.93
Test statistic : [tex]t=\dfrac{\overline{x}-\mu}{\dfrac{s}{\sqrt{n}}}[/tex]
i.e. [tex]t=\dfrac{7.24-7}{\dfrac{1.93}{\sqrt{22}}}\approx0.58[/tex]
For significance level [tex]\alpha=0.05[/tex] and degree of freedom 21 (df=n-1),
Critical t-value for left-tailed test= [tex]t_{\alpha, df}=t_{0.05,21}=- 1.7207[/tex]
Decision : Since the test statistic value (0.58) > critical value 1.7207, it means we are failed to reject the null hypothesis .
[Note : When [tex]|t_{cal}|>|t_{cri}|[/tex], then we accept the null hypothesis.]
Conclusion: We have sufficient evidence to reject the claim that LTCC Intermediate Algebra students get less than seven hours of sleep per night, on average.
