u wish to test the following claim (HaHa) at a significance level of α=0.02α=0.02.       Ho:μ=55.8Ho:μ=55.8       Ha:μ>55.8Ha:μ>55.8 You believe the population is normally distributed, but you do not know the standard deviation. You obtain a sample of size n=29n=29 with a mean of M=68.4M=68.4 and a standard deviation of SD=18.3SD=18.3.

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You wish to test the following claim (HaHa) at a significance level of α=0.02α=0.02.

      Ho:μ=55.8Ho:μ=55.8
      Ha:μ>55.8Ha:μ>55.8

You believe the population is normally distributed, but you do not know the standard deviation. You obtain a sample of size n=29n=29 with a mean of M=68.4M=68.4 and a standard deviation of SD=18.3SD=18.3.

What is the critical value for this test?

***(Report answer accurate to three decimal places.)***
critical value = 

What is the test statistic for this sample?

**(Report answer accurate to three decimal places.)**


test statistic = 

The test statistic is...

  • in the critical region
  • not in the critical region



This test statistic leads to a decision to...

  • reject the null
  • accept the null
  • fail to reject the null



As such, the final conclusion is that...

  • There is sufficient evidence to warrant rejection of the claim that the population mean is greater than 55.8.
  • There is not sufficient evidence to warrant rejection of the claim that the population mean is greater than 55.8.
  • The sample data support the claim that the population mean is greater than 55.8.
  • There is not sufficient sample evidence to support the claim that the population mean is greater than 55.8.

Thank you!

Expert Solution
Step 1

As the population standard deviation is not known, we will use a t-test.

The null and alternative hypotheses are:

Ho: \mu = 55.8

Ha: \mu > 55.8

This corresponds to a right-tailed test.

The t-statistic is computed as follows:

Statistics homework question answer, step 1, image 1

Since it is observed that t = 3.708 > t_c = 2.154, the null hypothesis is rejected.

Since it is observed that , it is then concluded that the null hypothesis is rejected.

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