Can someone check my work again to see if i done this right: thank you hypothesis test The hypothesis scenario:

Can someone check my work again to see if i done this right: thank you

hypothesis test

The hypothesis scenario:

A doctor wants to know if the median BMI of a group of 100 patients with presumed overweight is equal to 30. (this is the medical value to know if you are overweight) Given the sample mean of 31.

Based on historical data, the doctor knows that these patients have a standard deviation of 5, so he uses this value as the standard deviation of the population in a Z test of 1 sample.

My explanation:

Null hypothesis H0: μ =30

Alternative Hypothesis H1; μ >30

You can put this in calculator

(31-30)/(5/√100)

=2

1-Norm.dist(2, true)

=0.02275

Norm.s.inv

=0.9772

Using the Z to P value calculator with α =0.05 and z=2, you get 0.9772

P value= 1−0.9772=0.0228

The P-value is significant at 5% and thus the null hypothesis is rejected at that point. We conclude that at 5% significance level, μ >30