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A store owner claims the average age of her customers is 28 years. She took a survey of 31 randomly selected customers and found the average age to be 30.7 years with a standard error of 1.818. Carry out a hypothesis test to determine if her claim is valid. (a) Which hypotheses should be tested?

```
H_(0):p=28 vs. H_(a):p!=28
H_(0):\mu =28 vs. H_(a):\mu >28
H_(0):\mu =30.7 vs. H_(a):\mu !=30.7
H_(0):\mu =28 vs. H_(a):\mu !=28
```

(b) Find the test statistic: (Use 4 decimals.) (c) What is the

`P`

-value? X (Use 4 decimals.) (d) What should the store owner conclude, for

`\alpha =0.05`

? Reject the initial claim of 28 years. There is insufficient evidence the mean customer age is different than 28 . Do not reject the initial claim of 28 years. There is insufficient evidence the mean customer age is different than 28 . Do not reject the initial claim of 28 years. There is sufficient evidence the mean customer age is different than 28 . Reject the initial claim of 28 years. There is sufficient evidence the mean customer age is different than 28 . (e) If mean customer age really is equal to 29.6 years, but you conclude it is equal to 28 years, which type of error did you make, if any? Type I error Both Type I and Type II error The p -value is correct; therefore no error was made Type II error