3. A new process has been developed for applying pho­ toresist to 125-mm silicon wafers used in manufac­ turing integrated circuits. Ten wafers were tested, and the following photoresist thickness measurements (in angstroms x 1,000) were observed: 13.3987, 13.3957, 13.3902, 13.4015, 13.4001, 13.3918, 13.3965, 13.3925, 13.3946, and 13.4002. a. Test the hypothesis that mean thickness is 13.4 x 1,000 A. Use a = 0.05 and assume a two-sided alternative. b. Find a 99% two-sided confidence interval on mean photoresist thickness. Assume that thickness is normally distributed.

a

The null hypothesis is  

The alternative hypothesis is  

The null hypothesis is rejected

b

The  99% confidence level is  

Step-by-step explanation:

From the question we are told that

  The sample size is  n =  10

   The  population mean is  

   The level of significance is  

   The  sample data is  

13.3987, 13.3957, 13.3902, 13.4015, 13.4001, 13.3918, 13.3965, 13.3925, 13.3946, and 13.4002

Generally the sample mean is mathematically represented as

=>    

Generally the sample standard deviation  is mathematically represented as

=>

=>  

The null hypothesis is  

The alternative hypothesis is  

Generally the test statistics is mathematically represented as

=>    

=>  

Generally the p-value is mathematically represented as

From the z-table  

So

So from the obtained value we see that

Hence the null hypothesis is rejected

Consider the b question

Given that the confidence level is  99%  then the level of significance is

=>

Generally from the normal distribution table critical value  of   is  

Generally the margin of error is mathematically represented as  

=>  

=>    

Generally the 99% confidence interval is mathematically represented as

=>  

7

step-by-step explanation: