Question

The absolute viscosity for sesame oil is supposed to average 0.0248 Pa⋅s at 50 ∘C. Suppose a food scientist collects a random sample of 3 quantities of sesame oil and computes the mean viscosity for his sample to be ?⎯⎯⎯=0.0252 Pa⋅sx¯=0.0252 Pa⋅s at 50 ∘C Assume that measurement errors are normally distributed and that the population standard deviation of sesame oil viscosity is known to be ?=0.0003 Pa⋅s

The scientist will use a one‑sample ?z‑test for a mean, at a significance level of ?=0.01α=0.01, to evaluate the null hypothesis, ?0:?=0.0248 Pa⋅sagainst the alternative hypothesis, ?1:?≠0.0248 Pa⋅s. Complete the scientist's analysis by calculating the value of the one-sample ?z‑statistic, the ?p‑value, and then deciding whether to reject the null hypothesis.

First, compute the ?z‑statistic, ?z. Provide your answer precise to two decimal places. Avoid rounding within calculations.

?=z=

Determine the ?-valueP-value of the test using either a table of standard normal critical values or software. Give your answer precise to four decimal places.

?=P=

Should the researcher reject his null hypothesis if his significance level is ?=0.01α=0.01?

a,Yes. Because the ?-valueP-value of the test is greater than the stated alpha level of 0.01, there is sufficient evidence to reject the null hypothesis that the mean viscosity of sesame oil is equal to 0.0248 Pa⋅s at 50 ∘C.to 0.0248 Pa⋅s at 50 ∘C.

b.No. Because the ?-valueP-value of the test is greater than the stated alpha level of 0.01, there is insufficient evidence to reject the null hypothesis that the mean viscosity of sesame oil is equal to 0.0248 Pa⋅s at 50 ∘C.to 0.0248 Pa⋅s at 50 ∘C.

c.No. Because the ?-valueP-value of the test is less than the stated alpha level of 0.01, there is insufficient evidence to reject the null hypothesis that the mean viscosity of sesame oil is equal to 0.0248 Pa⋅s at 50 ∘C.to 0.0248 Pa⋅s at 50 ∘C.

d.Yes. Because the ?-valueP-value of the test is less than the stated alpha level of 0.01, there is sufficient evidence to reject the null hypothesis that the mean viscosity of sesame oil is equal to 0.0248 Pa⋅s at 50 ∘C.

Answer 1

= 0.0252 sample meon = 0.0252 dim: To check whether absolute viscosity for sesame oil sa 0.0248 Pais or not. Given: sample size = n= 3 f sample standard deviation = sa population standard deviation Parameter : Let M be the population mean. the average viscosity for sesame oil let Mo be some specified value of so Mo -rc 0.000 3. =0.01 do here in M -0.0248. equal to uls Hypothesis : Ho : The ave average aboolute viscosity for accome oil is Šr does not differ significantly than to He: The average tox pesame oil is not equal to or differo significantly from Ho Mathematica tically, absolute vislosity Hot M = Mo vs Mii M & Mo.

HO: M= 0.0248 US HLE M +0.0248. s we use fiere as population Standard deviation is gien 2- test for testing hypothesis the

Jest statistics : Zeal=x-H NN(0,1) oin here under Ho M= 0.0248 Ical = 0.0252 – 0.0248 0.0003 13 - 2.3094 Ical = 2.31 Decipion : Reject Ho if szcal] Z«12. We consider 2012 because the test is two sided, here = 0.01 0.005 = Nie < So 20.005 = 2:58: so here Izcal I = 2.31 Do we fail to reject Ho 2012 = 2:58 Also we reject Ho if p-value <a Herep-value = 0·0209 > x= 0.01 do we fail to reject to concluion: The average viscosity of sesame oil absolute 0.0248 Pas. may be equal to

Ønowers: I statistic = Zcal Zcal = 2.31. pevalue P = 0·0209. Decision : b. No, Because the P-value of the festis greater then the stated alpha level of 0:01 there is insufficient evidence to reject the null hypothesis that the mean viscosity of sesame oil is equal to 0.0248. Pa's at 50°c.