Math  /  Data & Statistics

QuestionTest the claim that the mean GPA of night students is smaller than 3.4 at the 0.025 significance level. The null and alternative hypothesis would be: H0:μ3.4H0:p=0.85H0:p0.85H0:p0.85H0:μ=3.4H0:μ3.4H1:μ<3.4H1:p0.85H1:p>0.85H1:p<0.85H1:μ3.4H1:μ>3.4\begin{array}{cccccc} H_{0}: \mu \geq 3.4 & H_{0}: p=0.85 & H_{0}: p \leq 0.85 & H_{0}: p \geq 0.85 & H_{0}: \mu=3.4 & H_{0}: \mu \leq 3.4 \\ H_{1}: \mu<3.4 & H_{1}: p \neq 0.85 & H_{1}: p>0.85 & H_{1}: p<0.85 & H_{1}: \mu \neq 3.4 & H_{1}: \mu>3.4 \\ & & & & & \end{array}
The test is: \qquad
Based on a sample of 80 people, the sample mean GPA was 3.37 with a standard deviation of 0.06 The test statistic is: \square (to 2 decimals)
The pp-value is: \square (to 2 decimals)

Studdy Solution
The **test statistic** is approximately -4.48\textbf{-4.48}.
The **p*p*-value** is approximately 0.00\textbf{0.00}.
Since our *p*-value is less than our significance level (0.00<0.0250.00 < 0.025), we **reject the null hypothesis**.
There is sufficient evidence to support the claim that the mean GPA of night students is smaller than 3.4.

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