Question

Chapter 10: Coefidence Intervals and Hypothesis Tests Based on Two Samples Ilypothesis tests concerning two popalation means when data are paired 7. Apsychologist is studying the effect of belly stars on Sneetches. A random sample of four Sneetches is drawn and a test of self-image is given to each Sneetch before and after having their belly star status changed. (If the Sneetch initially had a star, it was removed; if they did not have a star, one was created on them using the patented "Star- off/Star-on procedure.) From the sample data below does it appear that changing belly star status increases the average self-image of Sneetches? Use a-0.10. Image Score Before 120 88100 25 Image Score After 130 100 110 155 Answer this question by performing a left-tailed hypothesis test regarding . Then complete the table below Ho: The null hypothesis: The alternative hypothesis: The type of test statistic: (choose one) The value of the test statistic: (Round to at least three decimal places.) The degrees of freedom The critical value at the 0.10 level of significance: Find bounds on the p-ralue (Round to at least three decimal places.) lower bound- upper bound Construct a 90% confidence interval on the population mean change in self-image associated with a star status change. (Round to at least three decimal places.) At the 0.10 level, does it appear that changing belly star status increases the average self-image of Sneetches?

Answer 1

$H_0:\mu _d=0$

$H_a:\mu _d<0$

Image scores before	Image scores After	d=Before-After
120	130	-10
88	100	-12
100	110	-10
25	55	-30

$\overline{X_d}=-15.5,S_d=9.71,n=4$

T-test statistic will be used

Test statistic:$T=\frac{\overline{X_d}}{\frac{S_d}{\sqrt{n}}}=\frac{-15.5}{\frac{9.71}{\sqrt{4}}}=-3.19$

df=4-1=3

Significance level:$\alpha =0.1$

the critical value for the one-tailed test = -12.92

Bound on p-value is 0.025 and 0.01