Answer:
The null hypothesis is rejected and research hypotheses is supported
Step-by-step explanation:
From the question we are told that
The population mean is [tex]\mu = 30[/tex]
The standard deviation is [tex]\sigma = 5[/tex]
The sample size is n = 1
The cutoff Z score for significance is [tex]Z_{\alpha } = 1.96[/tex]
The mean score is [tex]\= x = 45[/tex]
Generally the test hypothesis is mathematically represented as
[tex]t = \frac{\= x - \mu }{ \frac{ \sigma }{\sqrt{n} } }[/tex]
=> [tex]t = \frac{45 - 30 }{ \frac{ 5}{\sqrt{1} } }[/tex]
=> [tex]t = 3[/tex]
From the obtained value we can see that [tex]t > Z_{\alpha }[/tex]
Hence the null hypothesis is rejected and research hypotheses is supported
