When fifteen vehicles were observed at random for their speeds (in M.P.H.) on a freeway, the following data were obtained.
61
53
57
55
62
58
60
54
62
60
59
66
55
54
63
Suppose that from past experience it may be assumed that vehicle speed is normally distributed with standard deviation of 3.96. Construct a 93 percent confidence interval for the true mean speed.
To construct a confidence interval for the true mean speed, we can use the following formula:
Confidence Interval = [Sample Mean - Margin of Error, Sample Mean + Margin of Error]
To calculate the margin of error, we need to know the standard deviation of the sample, which is given as 3.96.
First, let's calculate the sample mean:
Sample Mean = (Sum of all speeds)/Number of speeds
Sum of all speeds = 61 + 53 + 57 + 55 + ... + 54 + 63
Number of speeds = 15
Now, calculate the sum of all speeds and divide it by 15 to get the sample mean.
Next, let's calculate the margin of error using the following formula:
Margin of Error = (Critical Value) * (Standard Deviation / sqrt(Number of speeds))
Since we are constructing a 93 percent confidence interval, we need to find the critical value associated with a two-tailed test with a confidence level of 93 percent. The critical value can be found using a statistical table or online calculator.
Once you have the critical value and the sample mean, you can calculate the margin of error by plugging in the values into the formula.
Finally, substitute the sample mean and margin of error into the confidence interval formula to get the lower and upper bounds of the interval.
That's how you can construct a 93 percent confidence interval for the true mean speed using the given data.