Null Hypothesis: Is it being rejected?

Question

I was doing this particular question that is as following:

A drugs manufacturer claims that the amount of paracetamol in tablets is 60 mg. A sample of 10 tablets is taken and the amount of paracetamol in each is recorded:

59.1, 59.7, 61.0, 59.1,60.6,68.9,60.2,58.6,58.7,58.9

Assuming that this sample came from an underlying normal population, test the claim at 5% significance level that the amount of paracetamol is different from 60 mg.

I got my sample mean as 1512/25 and my unbiased variance as 7073/750

I set my null hypothesis as μ= 60 and my alternative hypothesis as μ ≠ 60 making it two tailed test

After doing the calculations, I got my test statistic as 0.494 and according to t-test, the tabulated value should be 2.262 when t(0.975,9).

Since 0.494 doesn't come in the rejection region, shouldn't we accept null hypothesis? But the answer says it is rejected. What am I doing wrong?

Answer 1

Below your data are imported into R, and a two-sided, one-sample t test is done in R. Your test statistic and conclusion not to reject are correct:

x = c(59.1, 59.7, 61.0, 59.1,60.6,68.9,60.2,58.6,58.7,58.9)
t.test(x, mu=60)


        One Sample t-test

data:  x
t = 0.49428, df = 9, p-value = 0.633
alternative hypothesis: true mean is not equal to 60
95 percent confidence interval:
  58.28318 62.67682
sample estimates:
mean of x 
    60.48 

If your book says you should reject, then either the data are not correct or this is one case (out of many) where an answer key is wrong.