A random sample of size 12 from a normal population is given below. 69 74 75 76 78 79 81 83 83 85 86 87

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Question: A random sample of size 12 from a normal population is given below.
69 74 75 76 78 79 81 83 83 85 86 87
a) Someone claimed that s = 10. Does this data set support the claim? Test at a = 0.05.
b) Test if the population mean is 85 using a = 0.05.
c) Find the p-value of the test

we are given that : random sample of size 13 from a normal population.

Part a) We have test if standard deviation is  10 or not ?

Thus we use following steps:

1) State H0 and Ha

H_{0}: \sigma = 10

Vs

H_{1}: \sigma \neq 10

2) Find test statistic:

We use chi squares test statistic to test the variance or standard deviation

Thus test statistic is given by:

\chi ^{2}=\frac{(n-1) \times s^{2}}{\sigma^{2}}

which follows chi square distribution with  n – 1 degrees of freedom

Where S2 =sample variance. Thus we need to find sample variance S2