a company produced ethyl el alcohol and claimed to jave a mean alcohol content of 70%.A random sample of 80 of ethyl alcohol bottles was taken as sample to verify this claim.it was found out that the mean alcohol content is 65% with a standard deviation of 2%. test the claim at 5% level of significance and assume that the population is normallt distributed
Given claim
The mean alcohol content in ethyl alcohol produced by company is of 70%.
The null and alternate hypothesis are shown below
The sample mean alcohol content is and standard deviation is σ=2%
The level of significance is 5%.
The population is normally distributed and as the sample size is high the sample is also treated as normally distributed.
The test statistic is calculated as shown below
This is a two tailed hypothesis test.
With respect to Z table we get P(Z<-2.5)=0.0062
So p value is calculated as shown below
The p-value 0.0124 is less than the level of significance 0.05 or 5%. Thus we have sufficient evidence to reject the null hypothesis. So we conclude that the alcohol content in ethyl alcohol produced by company is not 70%.
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