Question

In: Statistics and Probability

A researcher claims that the average wind speed in his city is 10 miles per hour....

A researcher claims that the average wind speed in his city is 10 miles per hour. In a random sample of 36 days, you found the average speed of wind is 10.2 with a standard deviation of 0.8 miles per hour. At α=0.05 is there enough evidence to say that the average is greater than the researcher’s claim. Show your work by using hypothesis testing.

Expert Solution

Step 1:

Ho: = 10

Ha: > 10

Null hypothesis states that the average wind speed in the city is 10 miles per hour.

Alternative hypothesis states that the average wind speed in the city is greater 10 miles per hour.

Step 2: Test statistics

n = 36

sample mean = 10.2

sample sd = 0.8

Assuming that the data is normally distributed and also as the population sd is not given, we will calculate t stat

Step 3:

df = 36-1 = 35

= 0.05

t-critical value for a right-tailed test, for a significance level of α=0.05 is tc=1.69

As the t stat (1.5) does not fall in the rejection area, we fail to reject the Null hypothesis.

Hence we do not have sufficient evidence to believe that the average wind speed in the city is greater 10 miles per hour.

orchestra answered 2 years ago

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