Question

Question 12 3 pts CANCER SURVIVAL Write out in words, in context, what making such an error would mean. We would not be accepting that the average survival time was different from 200 days, when it was indeed different from 200. We would be accepting that the average survival time was different from 200 days, when it was really not different from 200 days. We would not be accepting that the average survival time was different from 200 days, when it was really not different from 200 days. We would be accepting that the average survival time was different from 200 days, when it was indeed different from 200.

Answer 1

Let Ho: The average survival time was 200 and H1: The average survival time was different from 200.

1. P(not Accepting H1|H1 is true) = P(accepting Ho|it is false) = Type II Error

2. P(accepting H1|H1 was false) = P(accepting H1|Ho was true) = P(rejecting Ho|Ho was true) = Type I error

3. P(not accepting H1|H1 was false) = P(accepting Ho|Ho was true) = no error made

4. P(accepting H1|H1 was true) = no error made

5. Sample : 20, 37, 63, 64, 72, 81, 138, 151,155,166,166,223,245,246,450,459

mean = 171

sample standard deviation = 131.1884

sample size = 16

Now:

The provided sample mean = 171 and the sample standard deviation is s = 131.1884, and the sample size is n = 16

(1) Null and Alternative Hypotheses

The following null and alternative hypotheses need to be tested:

Ho: μ = 200

Ha: μ ≠ 200

This corresponds to a two-tailed test, for which a t-test for one mean, with unknown population standard deviation will be used.

(2) Rejection Region

Based on the information provided, the significance level is \alpha = 0.05α=0.05, and the critical value for a two-tailed test is tc​=2.131.

The rejection region for this two-tailed test is R={t:∣t∣>2.131}

(3) Test Statistics

The t-statistic is computed as follows:

X - μo t= 171 – 200 131.1884 16 -0.884 s/n

(4) Decision about the null hypothesis

Since it is observed that ∣t∣=0.884≤tc​=2.131, it is then concluded that the null hypothesis is not rejected.

Using the P-value approach: The p-value is p=0.3905, and since p=0.3905≥0.05, it is concluded that the null hypothesis is not rejected.

(5) Conclusion

It is concluded that the null hypothesis Ho is not rejected. Therefore, there is not enough evidence to claim that the population mean μ is different than 200, at the 0.05 significance level. or The average survival time is 200 days

Confidence Interval

The 95% confidence interval is 101.095<μ<240.905. days

Graphically

$normaldistributiongrapher.php?mean=0&sig$

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