18. To test H0: = 45 versus H1: 45, a rando size n = 40 is obtained from a popul

Question

18. To test H0: = 45 versus H1: 45, a rando size n = 40 is obtained from a population whosestape deviation is known to be 8. (a) Does the population need to be normally distributed to (b) If the sample mean is determined to be x 48.3, com- (c) If the researcher decides to test this hypothesis at the (d) Construct a 95% confidence interval to test the compute the P-value? pute and interpret the P-value. = 0.05 level of significance, will the researcher reject the null hypothesis? Why? hypothesis.

Explanation / Answer

a) No' from central limit theorum as sample size is greater then 30 ; therefore sample mean is normally distributed.

b)

here std error of mean =std deviation/(n)1/2 =8/(40)1/2 =1.2649

therfore test statistic z =(Xbar-mean)/std error =(48.3-45)/1.2649=2.6089

for above test statistic ; p value =0.0091

here p value is probability of getting above or more extreme absolute test statistic value given mean value is 45.

c) as p value is less then 0.05 level of significance; we reject null hypothesis.

d) for 95% confidence interval ; critical value of z =1.96

therefore 95% confidence interval =sample mean -/+ z*std error =45.8208 ; 50.7792

above interval gives 95% confidence to contain true population mean of given distribution

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