Psychology stats The producers of a new toothpaste claim that it prevents more c

Question

Psychology stats

The producers of a new toothpaste claim that it prevents more cavities than other brands of toothpaste. A random sample of 60 people used the new toothpaste for 6 months. The mean number of cavities at their next checkup is 1.5. In the general population, the mean number of cavities at a 6-month checkup is 1.73 ( = 1.12).

a. Is this a one- or two-tailed test?

b. What are H0 and Ha for this study?

c. Compute zobt.

d. What is zcv?

e. Should H0 be rejected? What should the researcher conclude?

f. Determine the 95% confidence interval for the population mean, based on the sample mean.

Explanation / Answer

a) one tailed

b) Ho mean =1.73

Ha: mean <1.73

c) std error=std deviation/(n)1/2 =1.12/sqrt(60)=0.1446

hence zobt=(X-mean)/std error =(1.5-1.73)/0.1446=-1.5906

d) zcv for 0.05 level =1.64485

e)as zobt is higher then zcv we can not reject null hypothesis. Hence we can not accept producer claim

f) for 95% CI, z=1.96

hence Confidence interval =sample mean +/- z*std error =1.2166 ; 1.7834

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