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(solution) The director of manufacturing at a textile mill needs to


The director of manufacturing at a textile mill needs to determine whether a new machine is producing a particular type of cloth according to the manufacturer's specifications, which indicate that the cloth should have a mean breaking strength of 40 kgs. The standard deviation is known to be 4 kgs. A sample of 49 pieces of cloth reveals a mean breaking strength of 39.1 kgs. 

Is there evidence that the mean breaking strength is less than 40 kgs? Use a 1% test.


The population parameter of interest is

Answer 1Choose...? < 40reject H0µ ? 400.01z_stat is greater than 2.3263the mean breaking strength of all cloth0.11420.10do not reject H0z_stat is less than -2.3263 or z_stat is greater than 2.3263insufficient evidence at the 1% significance level to conclude that the mean breaking strength is less than 40 kgsµ ? 40z_stat is less than -2.3263-1.58sufficient evidence at the 1% significance level to conclude that the mean breaking strength is less than 40 kgs0.05? > 400.05711.58

The null hypothesis is

Answer 2Choose...? < 40reject H0µ ? 400.01z_stat is greater than 2.3263the mean breaking strength of all cloth0.11420.10do not reject H0z_stat is less than -2.3263 or z_stat is greater than 2.3263insufficient evidence at the 1% significance level to conclude that the mean breaking strength is less than 40 kgsµ ? 40z_stat is less than -2.3263-1.58sufficient evidence at the 1% significance level to conclude that the mean breaking strength is less than 40 kgs0.05? > 400.05711.58

The alternative hypothesis is

Answer 3Choose...? < 40reject H0µ ? 400.01z_stat is greater than 2.3263the mean breaking strength of all cloth0.11420.10do not reject H0z_stat is less than -2.3263 or z_stat is greater than 2.3263insufficient evidence at the 1% significance level to conclude that the mean breaking strength is less than 40 kgsµ ? 40z_stat is less than -2.3263-1.58sufficient evidence at the 1% significance level to conclude that the mean breaking strength is less than 40 kgs0.05? > 400.05711.58

The level of significance is

Answer 4Choose...? < 40reject H0µ ? 400.01z_stat is greater than 2.3263the mean breaking strength of all cloth0.11420.10do not reject H0z_stat is less than -2.3263 or z_stat is greater than 2.3263insufficient evidence at the 1% significance level to conclude that the mean breaking strength is less than 40 kgsµ ? 40z_stat is less than -2.3263-1.58sufficient evidence at the 1% significance level to conclude that the mean breaking strength is less than 40 kgs0.05? > 400.05711.58

H0 will be rejected if

Answer 5Choose...? < 40reject H0µ ? 400.01z_stat is greater than 2.3263the mean breaking strength of all cloth0.11420.10do not reject H0z_stat is less than -2.3263 or z_stat is greater than 2.3263insufficient evidence at the 1% significance level to conclude that the mean breaking strength is less than 40 kgsµ ? 40z_stat is less than -2.3263-1.58sufficient evidence at the 1% significance level to conclude that the mean breaking strength is less than 40 kgs0.05? > 400.05711.58

The test statistic is

Answer 6Choose...? < 40reject H0µ ? 400.01z_stat is greater than 2.3263the mean breaking strength of all cloth0.11420.10do not reject H0z_stat is less than -2.3263 or z_stat is greater than 2.3263insufficient evidence at the 1% significance level to conclude that the mean breaking strength is less than 40 kgsµ ? 40z_stat is less than -2.3263-1.58sufficient evidence at the 1% significance level to conclude that the mean breaking strength is less than 40 kgs0.05? > 400.05711.58

The p-value is

Answer 7Choose...? < 40reject H0µ ? 400.01z_stat is greater than 2.3263the mean breaking strength of all cloth0.11420.10do not reject H0z_stat is less than -2.3263 or z_stat is greater than 2.3263insufficient evidence at the 1% significance level to conclude that the mean breaking strength is less than 40 kgsµ ? 40z_stat is less than -2.3263-1.58sufficient evidence at the 1% significance level to conclude that the mean breaking strength is less than 40 kgs0.05? > 400.05711.58

The decision is

Answer 8Choose...? < 40reject H0µ ? 400.01z_stat is greater than 2.3263the mean breaking strength of all cloth0.11420.10do not reject H0z_stat is less than -2.3263 or z_stat is greater than 2.3263insufficient evidence at the 1% significance level to conclude that the mean breaking strength is less than 40 kgsµ ? 40z_stat is less than -2.3263-1.58sufficient evidence at the 1% significance level to conclude that the mean breaking strength is less than 40 kgs0.05? > 400.05711.58

Based on the sample, there is

Answer 9



 


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