Consider Ho: = 31 versus H;: u 31. A random sample of 16 observations taken from this population produced a sample mean of 25.71. The population is normally distributed with o= 9. Note: Use Table...

Extracted text: Consider Ho: = 31 versus H;: u 31. A random sample of 16 observations taken from this population produced a sample mean of 25.71. The population is normally distributed with o= 9. Note: Use Table IVinAppendix C to compute the probabilities. (a) Calculate the p-value. (b) Considering the p-value of part (a). would you reject the null hypothesis if the test were made at the significance level of 0.05? (c) Considering the p-value of part (a), would you reject the null hypothesis if the test were made at the significance level of 0.01? Recall the following from section 9.2 of the text. The p-value or probability-value approach. (1) We reject the null hypothesis if p-valuesa or a2p-value. We do not reject the null hypothesis if p-value > aor a< p-value. (2) for a one-tailed test, the p-value is given by the area in the tail of the sampling distribution curve beyond the observed value of the sample statistic. for a two-tailed test, the p-value is given by twice the area in the tail of the sampling distribution curve beyond the observed value of the sample statistic (3) to find the area in the tail of the sampling distribution curve (we use normal distribution here), we first find the value of z corresponding to the observed value of x using the formula: n = sample size, and uand o are the population mean and standard deviation. we call this z value the observed vn where o; = value of z 8th-ed chapter 09, section 9.2, intelligent tutoring problem 018 consider ho: = 31 versus h;: u 31. arandom sample of 16 observations taken from this population produced a sample mean of 25.71. the population is normally distributed with o =9. (a) compute oz. round the answer to four decimal places. oz = (b) compute z value. round the answer to two decimal places. (c) find area to the left of z-value on the standard normal distribution. round the answer to four decimal places. the area = (d) find p-value. round the answer to four decimal places. p-value = p-value.="" (2)="" for="" a="" one-tailed="" test,="" the="" p-value="" is="" given="" by="" the="" area="" in="" the="" tail="" of="" the="" sampling="" distribution="" curve="" beyond="" the="" observed="" value="" of="" the="" sample="" statistic.="" for="" a="" two-tailed="" test,="" the="" p-value="" is="" given="" by="" twice="" the="" area="" in="" the="" tail="" of="" the="" sampling="" distribution="" curve="" beyond="" the="" observed="" value="" of="" the="" sample="" statistic="" (3)="" to="" find="" the="" area="" in="" the="" tail="" of="" the="" sampling="" distribution="" curve="" (we="" use="" normal="" distribution="" here),="" we="" first="" find="" the="" value="" of="" z="" corresponding="" to="" the="" observed="" value="" of="" x="" using="" the="" formula:="" n="sample" size,="" and="" uand="" o="" are="" the="" population="" mean="" and="" standard="" deviation.="" we="" call="" this="" z="" value="" the="" observed="" vn="" where="" o;="value" of="" z="" 8th-ed="" chapter="" 09,="" section="" 9.2,="" intelligent="" tutoring="" problem="" 018="" consider="" ho:="31" versus="" h;:="" u="" 31.="" arandom="" sample="" of="" 16="" observations="" taken="" from="" this="" population="" produced="" a="" sample="" mean="" of="" 25.71.="" the="" population="" is="" normally="" distributed="" with="" o="9." (a)="" compute="" oz.="" round="" the="" answer="" to="" four="" decimal="" places.="" oz="(b)" compute="" z="" value.="" round="" the="" answer="" to="" two="" decimal="" places.="" (c)="" find="" area="" to="" the="" left="" of="" z-value="" on="" the="" standard="" normal="" distribution.="" round="" the="" answer="" to="" four="" decimal="" places.="" the="" area="(d)" find="" p-value.="" round="" the="" answer="" to="" four="" decimal="" places.="" p-value="">