Let p3 have the inner product as in exercise 9, with p0, p1, and q the polynomials described there. find the best approximation to by polynomials in span . reference: let p3 have the inner product given by evaluation at

a) compute the orthogonal projection of p2 onto the subspace spanned by p0 and p1.
b) find a polynomial q that is orthogonal to p0 and p1, such that is an orthogonal basis for span scale the polynomial q so that its vector of values at .

According to a research study, parents with young children slept 6.4 hours each night last year, on average. a random sample of 18 parents with young children was surveyed and the mean amount of time per night each parent slept was 6.8. this data has a sample standard deviation of 0.9. (assume that the scores are normally distributed.) researchers conduct a one-mean hypothesis at the 5% significance level, to test if the mean amount of time parents with young children sleep per night is greater than the mean amount of time last year. the null and alternative hypotheses are h0: μ=6.4 and ha: μ> 6.4, which is a right-tailed test. the test statistic is determined to be t0=1.89 using the partial t-table below, determine the critical value(s). if there is only one critical value, leave the second answer box blank.