Hi I would like some help on my Statistics homework Thank yo

Hi I would like some help on my Statistics homework. Thank you!

The instructions are as follows:

-Write all given values

-State the null and alternative hypotheses

-Determine the level of significance,

-Determine the approproiate test statistic to be used and compute

-Determine the critical region and find its value

-Write your decision whether to reject or do not reject the null hypothesis, state your interpretation

Past experience indicates that the time required for high school seniors to complete a standardized test is a normal random variable with a mean of 35 minutes. If a random sample of 20 high school seniors took an average of 33.1 minutes to complete this test with a standard deviation of 4.3 minutes, test the hypothesis, at the 0.05 level of significance, that 35 minutes against the alternative that

Solution

Formulating the null and alternative hypotheses,              
              
Ho:   u   >=   35  
Ha:    u   <   35   [HYPOTHESES]

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As we can see, this is a    left   tailed test, AT 0.05 SIGNIFICANCE.

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Getting the test statistic, as              
              
X = sample mean =    33.1          
uo = hypothesized mean =    35          
n = sample size =    20          
s = standard deviation =    4.3          
              
Thus, t = (X - uo) * sqrt(n) / s =    -1.976060073   [ANSWER, TEST STATISTIC]

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Thus, getting the critical t,              

df = n - 1 =    19          

tcrit = -1.729132812      
              
Thus, the critical region is when t < -1.729132812.   [ANSWER, CRITICAL REGION]

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As t < 1.729132812, we   REJECT THE NULL HYPOTHESIS.  

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Thus, there is significant evidence that the mean time to compelete the test is less than 35 minutes. [CONCLUSION]