Historically, these bolts have an average thickness of 10.1 mm. A recent random sample of 10 bolts yielded these thicknesses:

9.7 9.9 10.3 10.1 10.5 9.4 9.9 10.1 9.7 10.3

a. Find the sample mean and standard deviation for these data.
b. Assume that the historical average is true. Calculate the observed value of the t-statistic.
c. What is the probability of these statistics (or worse) if the true mean were 10.1 mm?

a) Sample mean = 9.99

Sample standard deviation = 0.3348

b) -1.0389

c) 0.1631

Step-by-step explanation:

We are given the following in the question:

9.7, 9.9, 10.3, 10.1, 10.5, 9.4, 9.9, 10.1, 9.7, 10.3

a) sample mean and standard deviation

Formula:

where are data points, is the mean and n is the number of observations.  

Sum of squares of differences = 1.009

b) observed value of the t-statistic

Formula:

Putting all the values, we have

c) probability of these statistics (or worse) if the true mean were 10.1 mm

Degree of freedom =  n - 1 = 9

Calculating the value from the table

0.1631 is the the probability of these statistics (or worse) if the true mean were 10.1 mm

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step-by-step explanation:

answer is 144

step-by-step explanation: