(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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