Question

Indicate calculator functions used (ie T-Test, 2-SampTTest, etc) as well as calculator entries

State your conclusions in terms of the context of the problem.

1. A health club manager claims that its members lose an average of 15 pounds during the first six months of membership.  A sample of 16 members of this health club showed that they lost on average 11.5 pounds during the first six months of membership with a standard deviation of 2.2 pounds.  Test at the 1% significance level if the mean weight loss during the first six months of their membership by all members of this health club is actually less than 15 pounds.  Assume the population is normally distributed.

State the null and alternate hypothesis in both symbols and words

Clearly label the 6 step approach

Answer 1

Answer Date: 02/04/2020 Step 1 To test the hypothesis is that the population mean weight loss during the first six months of their membership by all members of this health club is actually less than 15 pounds at 1% significance level. Step 2 The null and alternative hypothesis in symbol is, Ho: 1 =15 Ha: [<15 The null and alternative hypothesis in words is, The null hypothesis is that the population mean weight loss during the first six months of their membership by all members of this health club is actually 15 pounds.

The alternative hypothesis is that population mean weight loss during the first six months of their membership by all members of this health club is actually less than 15 pounds. Step 3 The t-test statistics is, 1) By using TI-84 calculator, find t-test statistics with the help of following steps: Click ON. Select 1:Edit from EDIT. Enter Data. Select TESTS from Stat menu. 3) Select T Test from TESTS variables. 4) Enter Hypothesized mean (15), Sample mean (11.5), Standard deviation (2.2) and n (16) and select Alternative from T Test. 5) Select Alternative from Hypotheses. 6) Press Calculate.

T-Test t=-6.363636364 1335E-6 I + LIXUS EV | IIII XII M Il MADON . From TI-84 calculator output, the t-test statistics is - 6.364 | Step 4 The p-value for this test is, From TI-84 calculator output, the p-value for this test is 0.0000 Step 5 Decision

The conclusion is that the p-value in this context is less than 0.01 which is 0.0000, so the null hypothesis is rejected at 1% level of significance. Step 6 Decision There is sufficient evidence to indicate that the population mean weight loss during the first six months of their membership by all members of this health club is actually less than 15 pounds. The result is statistically significant.