Question

Choose the data set from at least one of your classmates. Use a 0.05 significance level to test the claim that was made about the average high temperature using the data set provided by this classmate. Note that we will treat this data set as a random sample, representing all June days in the community. Show all steps, including your hypotheses, your critical values, your test statistic and your conclusion. Post a picture of your work. Was your classmate's guess correct? Explain.

Null hypothesis   85° F

90     

90     

86     

90     

91     

92     

93     

92     

92     

83     

80     

89     

92     

93     

81     

87     

88.86666667         Mean

4.344900565         Standard Deviation

Answer 1

Null Hypothesis H0: = 85° F

Altenative Hypothesis Ha:   85° F

Sample mean, = 88.86666667

Sample standard deviation s = 4.344900565

Since we do not know the true population standard deviation we will conduct one sample t test.

Standard error of mean, SE = s /  = 4.344900565 / = 0.7932667

Test statistic, t = ( - ) / SE =  (88.86666667 - 85) / 0.7932667 = 4.87

Degree of freedom = n-1 = 30-1 = 29

Critical values of t at df = 29 and 0.05 significance level is 2.045

Since, the calculated test statistic t is greater than critical value of 2.045, we reject null hypothesis H0.

There is sufficient evidence at 5% significance level to conclude that the true mean high temperature is not equal to 85° F.

Thus, there is a significant evidence from the data that classmate's guess is not correct.